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Does adding a constant to all rewards change the set of optimal policies in continuing tasks?
In continuing tasks, adding the same constant to all states does not affect the relative values of any states under any policies. The conclusions is then that, for episodic tasks, the optimal policies may change if one adds a large enough constant to all rewards.
Can scaling all the rewards by a fixed amount change the optimal policy of a MDP?
Any optimal policy found with reward shaping is the optimal policy for the original MDP. True, you can change the reward function without changing the optimal policy by either multiplying by a constant, adding a scalar, or a non-linear potential-based reward.
What is optimal policy in MDP?
In a finite Markov Decision Process (MDP), the optimal policy is defined as a policy that maximizes the value of all states at the same time¹. In other words, if an optimal policy exists, then the policy that maximizes the value of state s is the same as the policy that maximizes the value of state s’.
How do you find optimal policy?
Finding an Optimal policy : We find an optimal policy by maximizing over q*(s, a) i.e. our optimal state-action value function. We solve q*(s,a) and then we pick the action that gives us most optimal state-action value function(q*(s,a)).
Why is epsilon-greedy Q learning?
The epsilon-greedy approach selects the action with the highest estimated reward most of the time. The aim is to have a balance between exploration and exploitation. Exploration allows us to have some room for trying new things, sometimes contradicting what we have already learned.
What is epsilon in machine learning?
In short, epsilon-greedy means pick the current best option (“greedy”) most of the time, but pick a random option with a small (epsilon) probability sometimes. There are many other algorithms for the multi-armed bandit problem.
What is a policy in an MDP?
A policy is a way of defining the agent’s action selection with respect to the changes in the environment. A (probabilistic) policy on an MDP is a mapping from the state space to a distribution over the action space: π : S ×A→ [0,1].
Why is the optimal policy independent of the initial state?
The intuition behind the argument saying that the optimal policy is independent of initial state is the following: The optimal policy is defined by a function that selects an action for every possible state and actions in different states are independent.
How to prove that an optimal policy exists?
The expanded form of the Bellman optimality equations. This set of non-linear equations (as many as the number of states) is called the “Bellman optimality equations”. So, if an optimal policy exists, its values should satisfy this set of equations⁴. Therefore, to show that an optimal policy exists, one must prove the following two statements:
Why does the optimal policy exist in MDP?
Why does the optimal policy exist? In a finite Markov Decision Process (MDP), the optimal policy is defined as a policy that maximizes the value of all states at the same time¹.
Why does the optimal policy exist in reinforcement learning?
The famous introductory book of Sutt o n and Barto on reinforcement learning¹ takes the existence of optimal policies for granted and let this question unanswered. I had difficult times to believe them and be able to continue reading!