1. ai.stackexchange.com

    However, a greedy policy over a non-optimal value function is an improvement on the policy that resulted in that value function, which is shown by the policy improvement theorem. If you can solve the Bellman equation for the optimal value function - either as a system of simultaneous equations, or using iteration in Dynamic Programming, then ...
  2. towardsdatascience.com

    Note that if ε=0, the policy becomes the greedy policy, and if ε=1, always explore. k-Armed Bandits: See Bandits. Markov Decision Process (MDP): The Markov Property means that each state is dependent solely on its preceding state, the selected action taken from that state and the reward received immediately after that action was executed.
  3. baeldung.com

    Mar 18, 2024While learning, however, we use a stochastic policy. We use the Epsilon-greedy policy. This policy will choose a random action some epsilon percent of the time and otherwise will follow the greedy policy. In the case of Q-learning, doing this improves exploration of the state space during training but fully exploits the learned policy during ...
  4. ai.stackexchange.com

    The $\epsilon$-greedy policy is a policy that chooses the best action (i.e. the action associated with the highest value) with probability $1-\epsilon \in [0, 1]$ and a random action with probability $\epsilon $.The problem with $\epsilon$-greedy is that, when it chooses the random actions (i.e. with probability $\epsilon$), it chooses them uniformly (i.e. it considers all actions equally good ...
  5. baeldung.com

    Mar 24, 2023Q-learning is an off-policy algorithm. It estimates the reward for state-action pairs based on the optimal (greedy) policy, independent of the agent's actions. An off-policy algorithm approximates the optimal action-value function, independent of the policy. Besides, off-policy algorithms can update the estimated values using made up actions.
  6. incompleteideas.net

    By construction, the greedy policy meets the conditions of the policy improvement theorem , so we know that it is as good as, or better than, the original policy. The process of making a new policy that improves on an original policy, by making it greedy with respect to the value function of the original policy, is called policy improvement.
  7. Nov 18, 2023With its limited knowledge, following a Greedy Policy would mean it repeatedly receives a +1 reward for eating the cheese next to it. However, there are greater rewards out there. However, there ...
  8. stats.stackexchange.com

    In reinforcement learning, policy improvement is a part of an algorithm called policy iteration, which attempts to find approximate solutions to the Bellman optimality equations. Page-84, 85 in Sutton and Barto's book on RL mentions the following theorem: Policy Improvement Theorem. Given two deterministic policies $\pi$ and $\pi'$:
  9. PI framework by de ning the multi{step greedy improvements (Efroni et al., 2018a). These works overcome the 1{step greedy update by de ning an h{greedy policy (h 1) as the policy that, from every state, is optimal for htime steps. This new improvement operator amounts to solve an h{horizon optimal control problem, reducing to the standard 1{step
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  1. I would like to know if the optimal value function can also be defined as$$v_*(s_t) = \max_{a \in A(s_t)} \big\{ E_F \left[ r_{t+1} | s_t,a \right]+ \delta E_F \left[v_* \left(s_{t+1}\right)| s_t,a \right] \big\},$$

    This looks correct to me, although I am used to different notation, and viewing this after resolving the expectations. From Sutton & Barto, I would write the following:

    $$v^*(s) = \text{max}_a \sum_{r,s'}p(r,s'|s,a)(r + \gamma v^*(s'))$$

    which I think matches your equation term-for-term.

    To me, behaving greedily and chosing the optimal policy seem equivalent, which confuses me a bit.

    You have to take care with the self-reference to the optimal value function - it occurs on both sides of the Bellman equation.

    • Behaving greedily with respect to an optimal value function is an optimal policy.

    • Behaving greedily with respect to any other value function is a greedy policy, but may not be the optimal policy for that environment.

    • Behaving greedily with respect to a non-optimal value function is not the policy that the value function is for, and there is no Bellman equation that shows this relationship.

    • Only the optimal policy has Bellman equation that includes $\text{max}_a$. All others must use the more general $v_{\pi}(s) = \sum_a \pi(a|s) \sum_{r,s'}p(r,s'|s,a)(r + \gamma v_{\pi}(s'))$

    • However, a greedy policy over a non-optimal value function is an improvement on the policy that resulted in that value function, which is shown by the policy improvement theorem.

    If you can solve the Bellman equation for the optimal value function - either as a system of simultaneous equations, or using iteration in Dynamic Programming, then you will have the optimal value function and by implication behaving greedily with respect to it will be an optimal policy. This is the basis for Value Iteration.

    --Neil Slater

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