Benchmarking Tabular Reinforcement Studying Algorithms

posts, we explored Half I of the seminal ebook Reinforcement Studying by Sutton and Barto [1] (*). In that part, we delved into the three elementary methods underlying almost each fashionable Reinforcement Studying (RL) algorithm: Dynamic Programming (DP), Monte Carlo strategies (MC), and Temporal Distinction Studying (TD). We not solely mentioned algorithms from every subject in depth but in addition applied each in Python.

Half I of the ebook focuses on tabular answer strategies — approaches suited to issues sufficiently small to be represented in desk type. For example, with Q-learning, we will compute and retailer a whole Q-table containing each potential state-action pair. In distinction, Half II of Sutton’s ebook tackles approximate answer strategies. When state and motion areas turn out to be too giant — and even infinite — we should generalize. Take into account the problem of enjoying Atari video games: the state area is just too huge to mannequin exhaustively. As an alternative, deep neural networks are used to compress the state right into a latent vector, which then serves as the premise for an approximated worth perform [2].

Whereas we’ll enterprise into Half II in upcoming posts, I’m excited to announce a brand new collection: we are going to benchmark all of the algorithms launched in Half I towards each other. This publish serves each as a abstract and an introduction to our benchmarking framework. We’ll consider every algorithm based mostly on how shortly and successfully it might remedy more and more bigger Gridworld environments. In future posts, we plan to increase our experiments to tougher eventualities, akin to two-player video games, the place the variations between these strategies shall be much more obvious.

Summarized, on this publish, we are going to:

Introduce the benchmark process and focus on our comparability standards.
Present a chapter-by-chapter abstract of the strategies launched in Sutton’s ebook together with preliminary benchmarking outcomes.
Determine the best-performing strategies from every group and deploy them in a larger-scale benchmarking experiment.

Desk of Contents

Introducing the Benchmark Activity and Experiment Planning

On this publish we’ll work with the Gymnasium [3] surroundings “Gridworld”. It’s primarily a maze-finding process, by which the agent has to get from the top-left nook of the maze to the bottom-right tile (the current) — with out falling into any of the icy lakes:

Picture by writer

The state area is a quantity between 0 and N — 1, the place N is the maximal variety of tiles (16 in our case). There are 4 actions the agent can execute in each step: going left, proper, up or down. Reaching the purpose yields reward 1, falling into the lake ends the episode with none reward.

The good factor about this surroundings is that one can generate random worlds of arbitrary measurement. Thus, what we’ll do with all strategies, is plot the variety of steps / updates wanted to unravel the surroundings versus the surroundings measurement. In truth, Sutton does this in some elements of the ebook, too, so we will consult with that.

Preliminaries

I’d like to start out with some normal notes — hoping these will information you thru my thought course of.

It isn’t straightforward to check algorithms in a “truthful” means. When implementing the algorithms I primarily appeared for correctness, but in addition simplicity — that’s, I wished readers to simply have the ability to join the Python code with pseudocode from Sutton’s ebook. For “actual” use circumstances, one would absolutely optimize the code extra, and in addition use a big array of methods frequent in RL, akin to utilizing decaying exploration, optimistic initialization, studying price tuning, and extra. Additional, one would take nice care to tune the hyperparameters of the deployed algorithm.

Utilized RL Methods

Because of the giant variety of algorithms underneath investigation, I can not do that right here. As an alternative, I recognized two necessary mechanisms, and measured their effectiveness on an algorithm recognized to work fairly properly: Q-learning. These are:

Intermediate rewards: as a substitute of solely rewarding the agent for reaching the purpose, we reward it for progress alongside the maze. We quantify this by the (normalized) distinction in x and y coordinates between present and former state. This makes use of the truth that the purpose in every Gridworld surroundings is at all times on the backside proper, and thus increased x / y coordinates often are higher (though one may nonetheless get “caught”, in case an icy lake is between the agent and the purpose). Since this distinction is normalized by the variety of states, its contribution is small, s.t. it doesn’t overshadow the reward of reaching the purpose.
Decaying exploration: all through this publish collection, the exploration-exploration dilemma got here up continuously. It describes the trade-off of exploiting states / actions already recognized to be good, and exploring much less explored states — doubtlessly discovering even higher options, on the threat of losing time in much less optimum areas. One frequent approach addressing that is to decay exploration: beginning with a excessive quantity of exploration early, and slowly decaying this all the way down to decrease ranges. We do that by linearly decaying ε from 1 (100% random exploration) to 0.05 over 1000 steps.

Let’s take a look at how Q-learning performs with these methods:

As we will see, within the baseline setup the variety of steps wanted shortly grows, and reaches the maximal variety of allowed steps (100.000 ) — which means the algorithm didn’t remedy the surroundings within the allotted variety of steps. Additionally decaying ε alone didn’t contribute a lot. Nevertheless, including intermediate rewards proved to be extraordinarily efficient — and the mix of this and decaying ε carried out finest.

Thus, for many strategies to return we begin with the “naïve” surroundings, the baseline implementation. Later we present outcomes for the “improved” surroundings consisting of intermediate rewards and decaying exploration.

Comparability Standards

As was seen within the earlier part I selected the variety of steps wanted till the discovered coverage solves the Gridworld surroundings because the default means of evaluating strategies. This appears a bit extra truthful than simply measuring elapsed time, since time relies on the concrete implementation (much like the idea of Big O notation)— and, as talked about above, I didn’t optimize for velocity. Nevertheless, you will need to be aware that additionally steps might be deceptive, as e.g. one step in DP strategies incorporates a loop over all states, whereas one step in MC and TD strategies is the technology in a single episode (really for TD strategies we often rely one step as one worth replace, i.e. an episode technology consists of a number of steps — nevertheless I made this extra similar to MC strategies on goal). On account of this we additionally present elapsed time typically.

Experiment Construction

To cut back the variance, for every Gridworld measurement we run every technique thrice, after which save the bottom variety of steps wanted.

The code required to run all following benchmarking might be discovered on GitHub.

Recap and Benchmarking of All Algorithms

With the basics out of the way in which, let’s correctly get began. On this part we are going to recap all launched algorithms from Half I of Sutton’s ebook. Additional, we are going to benchmark them towards one another on the beforehand launched Gridworld process.

Dynamic Programming

We begin with Chapter 4 of Sutton’s ebook, describing strategies from DP. These might be utilized to all kinds of issues, at all times constructing on the precept of iteratively constructing bigger options from smaller subproblems. Within the context of RL, DP strategies keep a Q-table which is crammed out incrementally. For this, we require a mannequin of the surroundings, after which, utilizing this mannequin, replace the anticipated worth of states or state-action pairs relying on the potential successor states. Sutton introduces two strategies we picked up in our corresponding publish: coverage and worth iteration.

Let’s begin with coverage iteration. This consists of two interleaved steps, particularly coverage analysis and coverage enchancment. Coverage analysis makes use of DP to — because the title says — consider the present coverage: we incrementally replace the state estimates through the use of the mannequin and coverage. Subsequent comes coverage enchancment, which employs a elementary idea of RL: in line with the coverage enchancment theorem, any coverage will get higher when altering the anticipated motion in a single state to a greater motion. Following this, we assemble the brand new coverage from the Q-table in grasping style. That is repeated, till the coverage has converged.

The corresponding pseudocode seems to be as follows:

Let’s come to worth iteration. That is similar to coverage iteration, however with a easy, but essential modification: in each loop, just one step of coverage analysis is run. It may be proven that this nonetheless converges to the optimum coverage, and general does so quicker than coverage iteration:

For extra particulars, right here’s my corresponding publish about DP strategies.

Outcomes

Now it’s time to see what these first two algorithms are actually fabricated from. We run the experiment sketched above, and get the next plot:

Each strategies are in a position to remedy all created Gridworld sizes within the minimal variety of steps, 100. Shocking? Properly, this really exhibits each a power and in addition to a weak point of DP strategies, as concurrently of our methodology: DP strategies are “thorough”, they require a whole mannequin of the world, after which iterate over all states — yielding an excellent answer with only a few passes over all states. Nevertheless, because of this all states must be estimated until convergence — regardless that a few of them is perhaps a lot much less attention-grabbing — and this scales fairly badly with the surroundings measurement. In truth, one measured step right here incorporates a full run over all states — indicating that for these strategies time is a greater measure.

For this, we get the next graph:

Now, we will see enhance in compute wanted w.r.t. to the variety of states. And, we will additionally see that, as claimed, worth iteration converges a lot quicker, and scales significantly better. Word that the x-axis labels denote n, with the Gridworld having a measurement of n x n.

Monte Carlo Strategies

Subsequent in our publish collection on RL we lined MC strategies. These can study from expertise alone, i.e. one can run them in any form of surroundings, with out having a mannequin of it — which is a surprising realization, and really helpful: typically, we don’t have this mannequin, different occasions, it could be too advanced and impractical to make use of. Take into account the sport of Blackjack: whereas we will actually mannequin all potential outcomes and corresponding chances, it’s a very tedious process — and studying to play by simply doing that could be a very tempting thought. On account of not utilizing a mannequin, MC strategies are unbiased — however on the draw back their expectation has a excessive variance.

One difficulty when implementing these strategies is ensuring that every one state-action pairs are repeatedly visited, and thus up to date. On account of not having a mannequin, we can not merely iterate over all potential mixtures (examine e.g. DP strategies), however (in a means) randomly discover the surroundings. If attributable to this we missed some states completely, we’d unfastened theoretical convergence ensures, which might translate into observe.

A method of satisfying that is the exploring begins assumption (ES): we begin every episode in a random state and select the primary motion randomly, too. Other than that, MC strategies might be applied somewhat merely: we merely play out full episodes, and set the anticipated worth of state-action pairs to the common obtained reward.

MC with ES seems to be as follows:

To take away the belief of ES, we will resort to 2 lessons of algorithms: on- and off-policy strategies. Let’s begin with the on-policy one.

That is really not too totally different from the ES algorithm, we merely use an ε-greedy coverage for producing episodes. That’s, we take away the belief of ES and use a “mushy” as a substitute of a “exhausting” coverage for producing episodes: the used coverage in each iteration just isn’t absolutely grasping, however ε-greedy — which ensures that within the restrict we see all potential state-action pairs:

Off-policy strategies observe the concept of splitting exploration and studying in two insurance policies. We keep a coverage π, which we wish to optimize, and a conduct coverage, b.

Nevertheless, we will’t merely use b in every single place in our algorithm. When producing an episode and computing returns, we acquire:

I.e., the ensuing worth is the anticipated worth of b, not π.

That is the place significance sampling is available in. We will repair this expectation with the fitting ratio:

This ratio is outlined by:

In our case, we acquire the next system:

(Word that this makes use of weighted significance sampling, as a substitute of “naïve” significance sampling.)

We may after all compute these ratios naively in each step. Nevertheless, Sutton introduces a intelligent scheme updating these values (denoted by W) incrementally, which is far more environment friendly. In truth, in my authentic publish I confirmed the naive model, too — I imagine this helps with understanding. Nevertheless, since right here we primarily care about benchmarking, and the “naïve” and the “incremental” model are equivalent, as much as efficiency — we right here solely checklist the marginally extra advanced incremental model.

In pseudocode the corresponding algorithm seems to be as follows:

Word that, against our preliminary publish introducing these strategies, the place the conduct coverage was merely randomly, right here we choose a greater one — particularly an ε-greedy one w.r.t. to the present Q-table.

For extra particulars right here’s my corresponding publish on MC strategies.

Outcomes

With that, let’s examine these three algorithms on small Gridworld environments. Word that one step right here denotes one full episode generated:

We observe off-policy MC to already day out at a Gridword measurement of 5×5, and, regardless that MC with ES and on-policy MC carry out higher, additionally they begin to battle with bigger sizes.

This is perhaps considerably stunning, and disappointing for MC followers. Don’t fear, we are going to handle to spice up this — nevertheless it exhibits a weak point of those algorithms: in “giant” environments with sparse rewards, MC strategies mainly should hope to bump into the purpose by probability — which decreases exponentially with the scale of the surroundings.

Thus, let’s attempt to make the duty simpler for the mannequin, and use the beforehand launched methods empirically discovered to assist efficiency of TD-learning: including intermediate rewards, and ε-decay — our “improved” setup.

In truth, with this all strategies fare significantly better:

Nevertheless, now MC ES is inflicting issues. Thus, let’s put this apart and proceed with out it: ES in any case was a theoretical idea on the way in which of growing MC strategies, and clunky to make use of / implement (some would possibly bear in mind how I applied having the surroundings begin in random states …):

Right here, not less than we get near the outcomes of DP. Word that I capped the maximal variety of steps to 100.000, so every time this quantity exhibits up within the graph it implies that the algorithm couldn’t remedy this surroundings within the given step restrict. On-policy MC really appears to carry out rather well, the variety of steps wanted barely will increase— however off-policy MC appears to carry out worse.

Dialogue

To me, MC strategies carry out surprisingly properly — since they primarily stumble across the surroundings randomly to start with, hoping to search out the purpose by exploration alone. Nevertheless, after all this isn’t absolutely true — their efficiency (talking of on-policy MC) turns into actually good solely after enabling intermediate rewards — which information the mannequin in direction of the purpose. On this setup it appears MC strategies carry out rather well — one potential cause being that they’re unbiased — and fewer delicate to hyperparameter tuning and co.

Temporal-Distinction Studying

Let’s come to TD strategies. These might be seen as combining the strengths of each approaches beforehand launched: much like MC, they don’t want a mannequin of the surroundings — however nonetheless they construct upon earlier estimates, they bootstrap — as in DP.

Let’s recap DP and MC fashions:

DP strategies flip the Bellman equation into an replace rule, and compute the worth of a state based mostly on the estimated values of its successor states:

MC strategies, however, play out full episodes after which replace their worth estimates based mostly on the noticed return:

TD strategies mix these two concepts. They play out full episodes, however after each step replace worth estimates with the noticed return, and the earlier estimate:

Among the most elementary RL algorithms stem from this subject — and we are going to focus on them within the following.

Let’s start with Sarsa. First, we modify above launched replace rule to work with state-action pairs:

With this, Sarsa is definitely launched somewhat shortly: we play episodes, and replace values following our present coverage. The title comes from the tuples used within the updates:

In pseudocode this seems to be as follows:

Subsequent up now we have Q-learning. That is similar to Sarsa, with one key distinction: it’s an off-policy algorithm. As an alternative of merely following the executed transition in the course of the replace, we take the utmost Q-value of all successor states:

You’ll be able to image this as making a conduct coverage b, which is the same as π, besides being grasping within the transitions underneath query.

The pseudocode seems to be like this:

One other algorithm is Anticipated Sarsa, which (you guessed it) — is an extension of Sarsa. As an alternative of following the one transition executed by the coverage, we account for all potential successor states, and weigh them by how probably they’re given the present coverage:

The final algorithm on this chapter is an extension of Q-learning. Q-learning suffers from an issue referred to as maximization bias: because it makes use of a most over anticipated values, the ensuing estimate can have optimistic bias. We will handle this through the use of two Q-tables: for every replace we use one for choosing a value-maximizing motion, and the opposite for computing the replace goal. Which is used the place is decided by a coin flip. The algorithm is called Double Q-learning:

Outcomes

Let’s take a look on the outcomes, beginning with the naïve surroundings:

We will see that each Q-learning strategies begin to get issues with Gridworld sizes of 11 x 11.

Thus let’s apply our recognized methods, yielding the “improved” setup:

All strategies can now discover options considerably faster — simply Anticipated Sarsa falls out. This might very properly be — it’s considerably much less used than Q-learning or Sarsa, and perhaps extra a theoretical idea.

Thus, let’s proceed with out this technique and see how giant world sizes we will remedy:

Q-learning can now additionally remedy grid sizes of 25 x 25 with out issues — however Sarsa and Double Q-learning begin to degrade.

Extra particulars might be present in my introductory publish about TD strategies.

Dialogue

Within the improved setup, TD strategies basically carry out properly. We solely eradicated Anticipated Sarsa early, which in any case just isn’t such a standard algorithm.

“Easy” Sarsa and Double Q-learning battle for bigger surroundings sizes, whereas Q-learning performs properly general. The latter is considerably stunning, since Double Q-learning ought to handle a number of the shortcomings of ordinary Q-learning, specifically the excessive variance. Doubtlessly, we already scale back the variance by working every experiment n occasions. One other speculation may very well be that Double Q-learning takes longer to converge, for the reason that variety of parameters has additionally doubled — which might point out that the facility of Double Q-learning exhibits higher for extra advanced issues with extra time.

As talked about performs Q-learning higher than Sarsa. This mirrors what can see in analysis / literature, particularly that Q-learning is considerably extra fashionable. This will most likely defined by it being off-policy, which often yields extra highly effective answer strategies. Sarsa however performs higher for stochastic or “harmful” duties: since in Sarsa the precise chosen motion is taken into consideration within the worth replace, it higher understands the results of its actions, which turns out to be useful for stochastic environments and / or environments the place one can, e.g., fall off a cliff. Regardless of the latter being the case right here, the surroundings might be not advanced or giant sufficient, that this impact comes into play.

TD-n

TD-n strategies in a means marry classical TD studying and MC strategies. As Sutton so properly places it, they “free us from the tyranny of the timestep” [1]. In MC strategies, we’re compelled to attend a full episode earlier than making any updates. In TD strategies, we replace estimates in each step — however are additionally compelled to solely look one step sooner or later.

Thus, it is sensible to introduce n-step returns:

With that, we will merely introduce Sarsa-n:

We play episodes following the present coverage, after which replace the worth estimates with the n-step return.

In my corresponding publish, we additionally introduce an off-policy model of this. Nevertheless, to not blow up this publish too lengthy, and destructive expertise with off-policy MC strategies, we concentrate on the “classics” — akin to Sarsa-n — and tree-n tree backup, which we introduce subsequent.

n-step tree backup is an extension of the beforehand seen Anticipated Sarsa. When computing the n-step return, the corresponding transition tree seems to be as follows:

I.e., there’s a single path down the tree comparable to the precise motion taken. Simply as in Anticipated Sarsa, we now wish to weigh actions in line with their likelihood decided by the coverage. However since now now we have a tree of depth > 1, the cumulative worth of later ranges is weighted by the likelihood of the motion taken to achieve these ranges:

The pseudocode seems to be as follows:

Right here’s my corresponding publish on n-step TD strategies.

Outcomes

As standard, we begin with the “naïve” setting, and procure the next outcomes:

Sarsa-n begins to battle already with smaller grid world sizes. Let’s see if the improved setup adjustments this:

Now certainly Sarsa-n performs significantly better, however n-step tree backup doesn’t.

Dialogue

I discovered this discovery sudden and considerably exhausting to clarify. I’d love to listen to your ideas on this — however within the meantime I used to be chatting with my chat agent of alternative, and got here to this speculation: intermediate rewards doubtlessly confuse the tree algorithm, because it must study an identical return distribution over all potential actions. Additional, the extra ε decays, the extra the anticipated distribution would possibly differ from the conduct coverage.

Mannequin-Based mostly Reinforcement Studying / Planning

Within the earlier chapter we mentioned the subject “planning” — within the RL context with this we primarily consult with model-based strategies. That’s: now we have (or construct) a mannequin of the surroundings, and use this mannequin to discover additional “nearly”, and specifically use these explorations for extra and higher updates / learnings of the worth perform. The next picture shows the combination of planning into studying very properly:

Within the top-right nook we see the “classical” RL coaching loop (additionally dubbed “direct” RL): beginning with some worth perform / coverage we act within the (actual) surroundings, and use this expertise to replace our price perform (or coverage within the case of policy-gradient strategies). When incorporating planning, we moreover additionally study a mannequin of the world from this expertise, after which use this mannequin to generate additional (digital) expertise, and replace our price or coverage perform from this.

This really is precisely the Dyna-Q algorithm, which seems to be as follows in pseudocode:

Steps (a) — (d) are our classical Q-learning, whereas the remainder of the algorithm provides the novel planning performance, specifically the world mannequin studying.

One other associated algorithm is Prioritized Sweeping, which adjustments how we pattern states for the “planning loop”: we discover and play in the actual surroundings, whereas studying the mannequin, and save state-action pairs with giant anticipated worth adjustments to a queue. Solely with this queue we begin the “planning loop”, i.e. one thing to the steps (e) and (f) above:

Extra particulars might be present in my earlier publish on model-based RL methods.

Outcomes

Let’s begin with the naïve setting:

Dyna Q performs fairly properly, whereas Prioritized Sweeping struggles early on.

Within the improved setting we see an analogous factor:

Dialogue

Prioritized sweeping already carried out poorly within the corresponding introductory publish — I think there both is a few difficulty, or extra probably this merely is a “tuning” factor — i.e. utilizing a improper sampling distribution.

Dyna-Q yields stable outcomes.

Benchmarking the Greatest Algorithms

Now we have now seen the efficiency of all algorithms from Half I of Sutton’s ebook by benchmarking them per chapter and on Gridworlds of as much as measurement 25 x 25. Already right here we noticed higher and worse performing algorithms, and specifically already discarded a couple of candidates not suited to bigger environments.

Now we wish to benchmark the remaining ones — the very best ones from every chapter — towards each other, on Gridworlds as much as measurement 50 x 50.

These algorithms are:

worth iteration
on-policy MC
Q-learning
Sarsa-n
Dyna-Q

Outcomes

Right here’s how they carry out on Gridworld, this time with a maximal step restrict of 200.000:

Let’s additionally plot the corresponding time wanted (be aware that I plot unsuccessful runs — runs reaching the maximal variety of steps with out producing a possible coverage — at 500s):

We will observe a number of attention-grabbing information from these figures:

The variety of steps vs. time wanted is very correlated.
Worth iteration performs exceptionally properly, fixing even Gridworlds of measurement 50 x 50 with ease, and doing so magnitudes quicker than the next-best algorithm.
The rating for the remaining algorithms is (higher to worse): On-policy MC, Dyna-Q, Q-learning, Sarsa-n.

Within the subsequent part we focus on these in additional particulars.

Dialogue

1. Steps vs. Time

We began this publish with a dialogue on which metrics / measurement to make use of, and — specifically — whether or not to make use of variety of steps or time wanted to unravel the issue. Trying again, we will say that this dialogue was not so related in spite of everything, and — considerably surprisingly — these two numbers are extremely correlated. That’s, even supposing, as initially described, one “step” can differ relying on the algorithm.

2. Worth Iteration Dominates

Worth Iteration carried out remarkably properly, fixing even giant Gridworlds (as much as 50×50) with ease—outpacing all different algorithms by a large margin. This is perhaps stunning, contemplating that DP strategies are sometimes thought of theoretical instruments, not often utilized in observe. Actual-world purposes are likely to favor strategies like Q-learning [2], PPO [4], or MCTS [5].

So why does such a “textbook” technique dominate right here? As a result of this surroundings is tailored for it:

The mannequin is absolutely recognized.
The dynamics are easy and deterministic.
The state area is comparatively small.

These are precisely the situations underneath which DP thrives. In distinction, model-free strategies like Q-learning are designed for settings the place such info is not obtainable. Their power lies in generality and scalability, not in exploiting small, well-defined issues. Q-learning incurs excessive variance and requires many episodes to converge—disadvantages which might be magnified in small-scale environments. Briefly, there’s a transparent trade-off between effectivity and generality. We’ll revisit this level in a future publish once we introduce perform approximation, the place Q-learning has extra room to shine.

3. A Rating Emerges

Past Worth Iteration, we noticed the next efficiency rating: On-policy MC > Dyna-Q > Q-learning > Sarsa-n

On-policy Monte Carlo emerged because the best-performing model-free algorithm. This matches with our earlier reasoning: MC strategies are easy, unbiased, and well-suited to issues with deterministic targets—particularly when episodes are comparatively brief. Whereas not scalable to giant or steady issues, MC strategies appear to be fairly efficient in small to medium-sized duties like Gridworld.

Dyna-Q comes subsequent. This end result reinforces our expectations: Dyna-Q blends model-based planning with model-free studying. Though the mannequin is realized (not given, as in Worth Iteration), it’s nonetheless easy and deterministic right here—making the realized mannequin helpful. This boosts efficiency considerably over pure model-free approaches.

Q-learning, whereas nonetheless highly effective, underperforms on this context for the explanations mentioned above: it’s a general-purpose algorithm that isn’t in a position to absolutely leverage the construction of easy environments.

Sarsa-n landed in final place. A probable rationalization is the added bias launched by means of bootstrapping in its multi-step updates. Not like Monte Carlo strategies, which estimate returns from full trajectories (unbiased), Sarsa-n makes use of bootstrapped estimates of future rewards. In small environments, this bias can outweigh the advantages of diminished variance.

Lastly, let’s examine our outcomes vs. those from Sutton:

Word that Sutton lists the overall variety of steps on the x-axis, whereas we checklist n, with the overall variety of states being n x n. For 376 states, Sutton report ~100k steps earlier than the optimum answer is discovered, whereas we report 75k for 400 states (20 x 20), contemplating Dyna-Q. The numbers are extremely comparable and supply a reassuring validation of our setup and implementation.

Conclusion

This publish served each as a recap of our collection on Half I of Sutton and Barto’s Reinforcement Studying [1]and as an extension past the ebook’s scope—by benchmarking all launched algorithms on more and more bigger Gridworld environments.

We started by outlining our benchmarking setup, then revisited the core chapters of Half I: Dynamic Programming, Monte Carlo strategies, Temporal-Distinction studying, and Mannequin-Based mostly RL / Planning. In every part, we launched key algorithms akin to Q-learning, supplied full Python implementations, and evaluated their efficiency on Gridworlds as much as measurement 25×25. The purpose of this preliminary spherical was to establish prime performers from every algorithmic household. Based mostly on our experiments, the standouts have been:
Worth Iteration, On-policy MC, Q-learning, Sarsa-n, and Dyna-Q. Python code to breed these outcomes, and specifically implementations of all mentioned strategies, is obtainable on GitHub.

Subsequent, we stress-tested these high-performers on bigger environments (as much as 50×50) and noticed the next rating:
Worth Iteration > On-policy MC > Dyna-Q > Q-learning > Sarsa-n

Whereas this end result could also be stunning—given the widespread use of Q-learning and the comparatively uncommon utility of Worth Iteration and MC strategies—it is sensible in context. Easy, fully-known, deterministic environments are perfect for Worth Iteration and MC strategies. In distinction, Q-learning is designed for extra advanced, unknown, and high-variance environments the place perform approximation turns into obligatory. As we mentioned, there’s a trade-off between effectivity in structured duties and generality in advanced ones.

That brings us to what’s subsequent. In upcoming posts, we’ll push the boundaries additional:

First, by benchmarking these strategies in tougher environments akin to two-player video games, the place direct competitors will expose their variations extra starkly.
Then, we’ll dive into Half II of Sutton’s ebook, the place perform approximation is launched. This unlocks the flexibility to scale reinforcement studying to environments far past what tabular strategies can deal with.

When you’ve made it this far—thanks for studying! I hope you loved this deep dive, and I’d like to have you ever again for the subsequent installment within the collection.