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MDPs and Reinforcement Learning

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# MDPs and Reinforcement Learning - PowerPoint PPT Presentation

MDPs and Reinforcement Learning. Overview. MDPs Reinforcement learning. Sequential decision problems. In an environment, find a sequence of actions in an uncertain environment that balance risks and rewards Markov Decision Process (MDP):

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### MDPs and Reinforcement Learning

Overview
• MDPs
• Reinforcement learning
Sequential decision problems
• In an environment, find a sequence of actions in an uncertain environment that balance risks and rewards
• Markov Decision Process (MDP):
• In a fully observable environment we know initial state (S0) and state transitions T(Si, Ak, Sj) = probability of reaching Sj from Si when doing Ak
• States have a reward associated with them R(Si)
• We can define a policy π that selects an action to perform given a state, i.e., π(Si)
• Applying a policy leads to a history of actions
• Goal: find policy maximizing expected utility of history
4x3 Grid World
• Assume R(s) = -0.04 except where marked
• Here’s an optimal policy
4x3 Grid World

Different default rewards produce different optimal policies

life=pain, get out quick

Life = struggle, go for +1, accept risk

Life = good, avoid exits

Life = ok, go for +1, minimize risk

Finite and infinite horizons
• Finite Horizon
• There’s a fixed time N when the game is over
• U([s1…sn]) = U([s1…sn…sk])
• Find a policy that takes that into account
• Infinite Horizon
• Game goes on forever
• The best policy for with a finite horizon can change over time: more complicated
Rewards
• The utility of a sequence is usually additive
• U([s0…s1]) = R(s0) + R(s1) + … R(sn)
• But future rewards might be discounted by a factor γ
• U([s0…s1]) = R(s0) + γ*R(s1) + γ2*R(s2)…+ γn*R(sn)
• Using discounted rewards
• Solves some technical difficulties with very long or infinite sequences and
• Is psychologically realistic
Value Functions
• The value of a state is the expected return starting from that state; depends on the agent’s policy:
• The value of taking an action in a stateunder policy p is the expected return starting from that state, taking that action, and thereafter following p :
Bellman Equation for a Policy p

The basic idea:

So:

Or, without the expectation operator: