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Understanding Agent Environment Interface using tic-tac-toe Most of you must have played the tic-tac-toe game in your childhood.
If not, you can grasp the rules of this simple game from its wiki page. Suppose tic-tac-toe is your favourite game, but you have nobody to play it with.
So you decide to design a bot that can play this game dynamic business planning you. Some key questions are: Can you define a rule-based framework to design an efficient bot?
You sure can, but you will have to hardcode a lot of rules for each of the possible situations that might arise in a game. However, an even more interesting question to answer is: Can you train the bot to learn by playing against you several times?
And that too without being explicitly programmed to play tic-tac-toe efficiently?
A few considerations for this are: First, the bot needs to understand the situation it is in. A tic-tac-toe has 9 spots to fill with an X or O.
Each different possible combination in the game will be a different situation for the bot, based on which it will make the next move. Each of these scenarios as shown in the below image is a different state. Consider the following situation encountered in tic-tac-toe: If bot X puts X in the bottom right position for example, it results in the following situation: Bot O would be rejoicing Yes!
They are programmed to show emotions as it can win the match with just one move. Now, we need to teach X not to do this again.
So we give a negative reward or punishment to reinforce the correct behaviour in the next trial. We say that this action in the given state would correspond to a negative reward and should not be considered as an optimal action in this situation.
Similarly, a positive reward would be conferred to X if it stops O from winning in the next move: Any random process in which the probability of being in a given state depends only on the previous state, is a markov process. State of the agent at time t At: Action taken by agent at time t Rt: The overall goal for the agent is to maximise the cumulative reward it receives in the long run.
Total reward at any time instant t is given by: In the above equation, we see that all future rewards have equal weight which might not be desirable. How good it is to be in a given state? Can we use the reward function defined at each time step to define how good it is, to be in a given state for a given policy?
The policy might also be deterministic when it tells you exactly what to do at each state and does not give probabilities. This optimal policy is then given by: How good an action is at a particular state? The above value function only characterizes a state.
Can we also know how good an action is at a particular state? A state-action value function, which is also called the q-value, does exactly that.
The value information from successor states is being transferred back to the current state Bellman was an applied mathematician who derived equations that help to solve an Markov Decision Process.
Unroll the value function equation to get: This is called the Bellman Expectation Equation. The value information from successor states is being transferred back to the current state, and this can be represented efficiently by something called a backup diagram as shown below.
The Bellman expectation equation averages over all the possibilities, weighting each by its probability of occurring. It states that the value of the start state must equal the discounted value of the expected next state, plus the reward expected along the way.
We have n number of states linear equations with unique solution to solve for each state s.A great business plan is a living, breathing blueprint for your business that can help you navigate and manage your company while also helping potential investors, partners, lenders, and others.
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