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HomeHomework Helpreinforcement-learningOptimal Value Functions

Optimal Value Functions

Optimal value functions represent the maximum expected returns achievable in a reinforcement learning environment, guiding the selection of policies that maximize cumulative rewards over finite or infinite horizons.

intermediate
3 hours
Reinforcement Learning
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Overview

Optimal value functions are crucial in reinforcement learning as they guide agents in making decisions that maximize expected returns. By understanding how to calculate and implement these functions, learners can develop more effective reinforcement learning models. The Bellman equation serves as a ...

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Key Terms

Value Function
A function that estimates the expected return from a given state.

Example: V(s) represents the value of state s.

Optimal Policy
A policy that yields the highest expected return from each state.

Example: π*(s) is the optimal action for state s.

Bellman Equation
A recursive equation that relates the value of a state to the values of its successor states.

Example: V(s) = R(s) + γ * Σ P(s'|s,a)V(s').

Discount Factor
A value between 0 and 1 that determines the importance of future rewards.

Example: A discount factor of 0.9 means future rewards are valued at 90%.

Markov Decision Process
A mathematical framework for modeling decision-making where outcomes are partly random and partly under the control of a decision maker.

Example: MDPs are used to define the environment in RL.

Exploration vs. Exploitation
The dilemma of choosing between exploring new actions and exploiting known rewarding actions.

Example: An agent must balance trying new strategies and using successful ones.

Related Topics

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Deep Reinforcement Learning
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Multi-Agent Reinforcement Learning
Study how multiple agents can learn and interact in shared environments.
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Key Concepts

Value FunctionOptimal PolicyBellman EquationDiscount Factor