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07-reinforcement

07-reinforcement - Reinforcement Learning Markov Decision...

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9/28/2009 1 Markov Decision Processes and Reinforcement Learning CS4700 – Fall 2009 Jesse Simons (based on notes by T. Joachims) Reinforcement Learning Problem Make sequence of decisions (policy) to get to goal / maximize utility Search Problems so far Known environment State space Consequences of actions Known utility / cost function First compute the sequence of decisions, then execute (potentially re- compute) Real-World Problems Environment is unknown a priori and needs to be explored Utility function unknown – only examples are available for some states No feedback on individual actions Learn to act and to assign blame/credit to individual actions Need to quickly react to unforeseen events (have learned what to do) Reinforcement Learning Issues – Agent can be passive (watch) or active (explore) Feedback (i.e. rewards) in terminal states only; or a bit of feedback in any state How to measure and estimate the utility of each action Environment fully observable, or partially observable Have model of environment and effects of action…or not Reinforcement Learning will address these issues! Markov Decision Process Representation of Environment: finite set of states S set of actions A for each state s in S Process At each discrete time step, the agent observes state s t in S and then chooses action a t in A. After that, the environment gives agent an immediate reward r t changes state to s t+1 (can be probabilistic) – Examples Markov Decision Process Model: Initial state: S 0 Transition function: T(s,a,s’) T(s,a,s’) is the probability of moving from state s to s’ when executing action a. Reward function: R(s) Real valued reward that the agent receives for entering state s. Assumptions Markov property: T(s,a,s’) and R(s) only depend on current state s, but not on any states visited earlier. Extension: Function R may be non-deterministic as well Utilities Rating a state sequence [s 0 , s 1 , s 2 , …] We want preferences to be stationary If [s 0 , s 1 , s 2 , …] better than [s 0 , s’ 1 , s’ 2 , …] implies [s 1 , s 2 , …] better than [s’ 1 , s’ 2 , …] Two ways for stationary utility Additive rewards: U h ([s 0 , s 1 , s 2 , …] ) = R(s 0 ) + R(s 1 ) + R(s 2 ) + … Discounted rewards: U h ([s 0 , s 1 , s 2 , …] ) = R(s 0 ) + γ R(s 1 ) + γ 2 R(s 2 ) + … Reward vs Utility
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9/28/2009 2 Example 2 3 - 1 + 1 0.8 0.1 0.1 Reward: In terminal states reward of +1 / -1 and agent gets “stuck” Each other state has a reward of -0.04.
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