Reinforcement Learning in the OpenAI Gym (Tutorial) - Off-policy Monte Carlo control
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Email Address Subscribe Monte Carlo Methods and Reinforcement Learning In this post, we're going to continue looking at Richard Sutton's book.
For the full list of posts up to this point, check There's a lot in chapter 5, so I thought it best to break it up into two posts, this one being part one.
TL;DR We take a look at Monte Carlo simulation for reinforcement learning with emphasis on first-visit Monte Carlo prediction algorithm and Monte Carlo prediction with exploring starts.
Over the past few weeks, I've posted a few other posts on the basics of Monte Carlo andand many of the same ideas from those posts come into play here when applied to reinforcement learning.
However, Monte Carlo methods differ from previous reinforcement learning methods we've looked at primarily because they rely lib envs blackjack on experience or sampled sequences of states, actions, and rewards instead of a model of the environment.
It requires no prior knowledge of lib envs blackjack environment's dynamics, simply access to it.
Policies also get changed when episodes are completed rather than in a step-by-step fashion.
These methods have a lot in common with the bandit problems that were previously explored and in that they take actions and average the rewards they recieve for their actions.
In essence, this class of algorithms really exhibits machine learning.
Monte Carlo Prediction Jumping into things, recall that the value of a state is the reward you expect to get when you're in that state.
We can estimate the value of a state by averaging the returns that we observe from visits to that state.
As more returns are observed, the average should converge to the true value of the state.
To go further we need to distinguish between first-visit MC and every-visit MC.
The distinction is important because they have different properties.
Blackjack can be formulated as an episodic finite MDP with each hand serving as an episode.
We can define rewards as +1, -1, and 0 in case you win, lose, or draw with the rewards coming at the end of the episode and being undiscounted.
The actions for the player are hit or stay with here defined as a player's hand and the cards they can see from the dealer.
Making the assumption that the deck is re-shuffled after every episode simplifies the situation by removing dependency on previous hands - so no advantage can be gained by counting cards.
We can use Monte Carlo methods to find the policy for this game through multiple simulations using a policy and averaging the returns from each state.
This is also an example of first-visit MC because a state cannot be returned to within an episode.
To demonstrate this, let's use OpenAI's gym library because they have a blackjack environment ready to go.
This helps so that we don't need to program the game ourselves.
We're using OpenAI Gym which has a number of built in functions in their environment.
We need to make the environment first by calling the correct environment, then once that is initialized, we're ready to play with it.
If you're familiar pa online blackjack OpenAI Gym, then skip ahead, otherwise we'll go through a few notes to familiarize yourself with the environments.
Once we set up the environment, we have a class with a number of different methods.
Many of these are standard across the OpenAI Gym library.
In the blackjack case, we have two discrete actions which are given by 0 or 1 for stick or hit.
Some environments have consistent starting states, others are stochastic.
In our blackjack case, we can pass it either 0 or 1 and we have the new state returned to us as well as other pertinent information regarding the game.
For the blackjack environment, each step returns a tuple of the current state with the values being the player's total score, the dealer's visible score, and whether or not the player has a usable ace.
The second value returned is the reward, the third value is whether the game is complete or not, and the final value is a dictionary object for additional information which is unused in this game.
With these basic methods in place, we should be able to run our MC simulation.
First, set up an array to hold the state-values which can be updated as we visit each one.
The state can be defined by three variables: the agent's score, the dealer's visible score, and whether or not the agent has a usable ace.
The simplest way to do this is to construct a 3-dimensional array of zeros which we can use to index those values.
The lib envs blackjack hand can range in value from 2-21 and the dealer's from 2-11.
This ought to make intuitive sense.
We essentially play the game thousands of times and record what happens.
We then average the rewards so we can estimate the value of each state that we may be in based on our experience.
In the case of blackjack, we can use the results as a betting guide to know when we are in a good position to win assuming you can place bets after a hand has started of course.
Thankfully, we've got other Monte Carlo algorithms in the bag to not only learn the values, but learn lib envs blackjack to play to maximize your reward.
Monte Carlo with Exploring Starts We turn now to the Monte Carlo with Exploring Starts MCES algorithm to accomplish our policy improvement goals.
This algorithm alternates between evaluation and improvement with each episode we play.
It continues in this manner until it gets to spreads blackjack bet end of the episode and then goes back to update the q-values and try again.
With the MCES version, we initialize our starting position randomly and with equal https://krimket.com/blackjack/casino-with-blackjack-tables-near-me.html across all states and then run the greedy algorithm again and again and again, until we reach convergence.
Then, we modify our policy according to the MCES algorithm outlined above.
We need to make a few modifications to our previous code.
Most notably, we're going to implement a 4-D array to capture the state-action pairs.
As before, we have the same three parameters to define our state, plus the action we take where 0 is to stand and 1 is to hit.
We need to certain that we're sampling from all of the potential starting points equally, which isn't actually the case in a game of blackjack.
As a result, we need to force the OpenAI environment to conform to this new sampling, hence overwriting the randomly generated starting points.
It also checks to see if the two-card total is 21 to force an ace to appear in the hand.
This causes a few more starting aces to be sampled lib envs blackjack both the player and dealer because we sample from totals which define the state rather than card combinations.
Once we've randomly initialized our starting state and initial action we play the game according to a greedy policy and update our initial results.
After half a million or so games, we can go ahead and visualize the results.
My algorithm surprisingly got better results standing on 17 without an ace and when looking at a dealer's ace than Sutton's, as well as when it had an ace totaling 17 and the dealer was showing a 6.
One thing that may have struck you as odd is that we sample all states with equal probability.
This isn't always possible to do particularly if you're working on a real data set nor is it very efficient.
You have to spend just as much time on the rare starting states as you do the very common ones, which means we're sampling from low-probabilities when we might be better served staying in the high-probability regions of our model.
In the next post in this series, we'll look at another Monte Carlo method which uses importance sampling to try to deal with this problem.
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r/ProRevenge - Blackjack dealer
Help on BlackjackEnv in module gym.envs.toy_text.blackjack object: class BlackjackEnv(gym.core.Env) | Simple blackjack environment | | Blackjack is a card聽...
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