But it still hasn't learned the optimal policy.

The bound is what does the optimal policy do?

That is, given a game, find the optimal policy.

So if it had learned the optimal policy, the policy loss would be zero, down here.

And from that, we can derive, look up, the optimal policy.

What does that mean? so that's the difference between the policy that the agent has learned and the optimal policy.

We can estimate the utility for some fixed policy, pi or we could estimate the Q values for the optimal policy while executing an exploration policy.

We're going to talk about game theory, which is the study of finding an optimal policy when that policy can depend on the opponent's policy and vice versa.

Finally, I'd like to ask you what is the optimal policy for the parameters we just studied.

And no matter what policy we have, it's not going to be better than the optimal policy and so we can only be making things worse with our policy, not making them better.

Rather than telling you how to compute the optimal policy, which assigns an action to each of these cells,

The pi that we want the optimal policy is the one that's going to maximize the discounted, total Reward.

Is it optimal?

A reinforcement learning agent can learn to explore the territory, find where the rewards are, and then learn an optimal policy.

Is that Pareto optimal?

So, now that we have a value backup function that we discussed in depth, the question now becomes what's the optimal policy?

Now what that suggests is the design for an exploration agent that will be more proactive about exploring the world when it's uncertain, and will fall back to exploiting the optimal policy or whatever policy it has as close to optimal when it becomes more certain about the world.

Policy

We kind of know that the optimal policy is to go south over here, so just really the value iteration for going south.

Now, is that optimal? No!

It can be sub optimal.

like the one over here and the on over here, have an optimal policy and action associated, because there is really no start state.

If you can calculate the optimal policy, that's okay, but in most cases you should deal with approximations, and calculating strategies might be useful.

First, we're keeping track of the optimal policy we've found so far and that gets updated as we go, and replaced with new policies.

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Fifteen is a pretty optimal number.

And in a single sentence, optimal decision making you really try to find the optimal decision.