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Berkeley COMPSCI 188 - Reinforcement Learning

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1CS 188: Artificial IntelligenceFall 2006Lecture 11: Reinforcement Learning10/3/2006Dan Klein – UC BerkeleyAnnouncements Midterm prep page is up Tell us NOW about midterm conflicts Project 2.1 up soon, due after midterm Project 1.4 (Learning Pacman) and the Pacmancontest will be after the midterm Review session this Sunday, details on webRecap: MDPs Markov decision processes: States S Actions A Transitions P(s’|s,a) (or T(s,a,s’)) Rewards R(s,a,s’) Start state s0 Quantities: Returns = sum of discounted rewards Values = expected future returns from a state (optimal, or for a fixed policy) Q-Values = expected future returns from a q-state (optimal, or for a fixed policy)ass, as,a,s’s’Reinforcement Learning Reinforcement learning: Still have an MDP: A set of states s ∈ S A set of actions (per state) A A model T(s,a,s’) A reward function R(s,a,s’) Still looking for a policy π(s) New twist: don’t know T or R I.e. don’t know which states are good or what the actions do Must actually try actions and states out to learn[DEMO]Example: Animal Learning RL studied experimentally for more than 60 years in psychology Rewards: food, pain, hunger, drugs, etc. Mechanisms and sophistication debated Example: foraging Bees learn near-optimal foraging plan in field of artificial flowers with controlled nectar supplies Bees have a direct neural connection from nectar intake measurement to motor planning areaExample: Backgammon Reward only for win / loss in terminal states, zero otherwise TD-Gammon learns a function approximation to V(s) using a neural network Combined with depth 3 search, one of the top 3 players in the world You could imagine training Pacman this way… … but it’s tricky!2Passive Learning Simplified task You don’t know the transitions T(s,a,s’) You don’t know the rewards R(s,a,s’) You are given a policy π(s) Goal: learn the state values (and maybe the model) In this case: No choice about what actions to take Just execute the policy and learn from experience We’ll get to the general case soonExample: Direct Estimation Episodes:xy(1,1) up -1(1,2) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(3,3) right -1(4,3) exit +100(done)(1,1) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(4,2) exit -100(done)U(1,1) ~ (92 + -106) / 2 = -7U(3,3) ~ (99 + 97 + -102) / 3 = 31.3γ = 1, R = -1+100-100Model-Based Learning Idea: Learn the model empirically (rather than values) Solve the MDP as if the learned model were correct Empirical model learning Simplest case: Count outcomes for each s,a Normalize to give estimate of T(s,a,s’) Discover R(s,a,s’) the first time we experience (s,a,s’) More complex learners are possible (e.g. if we know that all squares have related action outcomes, e.g. “stationary noise”)Example: Model-Based Learning Episodes:xyT(<3,3>, right, <4,3>) = 1 / 3T(<2,3>, right, <3,3>) = 2 / 2+100-100γ = 1(1,1) up -1(1,2) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(3,3) right -1(4,3) exit +100(done)(1,1) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(4,2) exit -100 (done)Model-Based Learning In general, want to learn the optimal policy, not evaluate a fixed policy Idea: adaptive dynamic programming Learn an initial model of the environment: Solve for the optimal policy for this model (value or policy iteration) Refine model through experience and repeat Crucial: we have to make sure we actually learn about all of the modelExample: Greedy ADP Imagine we find the lower path to the good exit first Some states will never be visited following this policy from (1,1) We’ll keep re-using this policy because following it never collects the regions of the model we need to learn the optimal policy ??3What Went Wrong? Problem with following optimal policy for current model: Never learn about better regions of the space if current policy neglects them Fundamental tradeoff: exploration vs. exploitation Exploration: must take actions with suboptimal estimates to discover new rewards and increase eventual utility Exploitation: once the true optimal policy is learned, exploration reduces utility Systems must explore in the beginning and exploit in the limit??Model-Free Learning Big idea: why bother learning T? Update each time we experience a transition Frequent outcomes will contribute more updates (over time) Temporal difference learning (TD) Policy still fixed! Move values toward value of whatever successor occursass, as,a,s’s’Example: Passive TDTake γ = 1, α = 0.5(1,1) up -1(1,2) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(3,3) right -1(4,3) exit +100(done)(1,1) up -1(1,2) up -1(1,3) right -1(2,3) right -1(3,3) right -1(3,2) up -1(4,2) exit -100(done)Problems with TD Value Learning TD value leaning is model-free for policy evaluation However, if we want to turn our value estimates into a policy, we’re sunk: Idea: learn Q-values directly Makes action selection model-free too!ass, as,a,s’s’Q-Learning Learn Q*(s,a) values Receive a sample (s,a,s’,r) Consider your old estimate: Consider your new sample estimate: Nudge the old estimate towards the new sample:Q-Learning Example [DEMO]4Q-Learning Properties Will converge to optimal policy If you explore enough If you make the learning rate small enough Neat property: does not learn policies which are optimal in the presence of action selection noiseESESExploration / Exploitation Several schemes for forcing exploration Simplest: random actions (ε-greedy) Every time step, flip a coin With probability ε, act randomly With probability 1-ε, act according to current policy Problems with random actions? You do explore the space, but keep thrashing around once learning is done One solution: lower ε over time Another solution: exploration functionsExploration Functions When to explore Random actions: explore a fixed amount Better idea: explore areas whose badness is not (yet) established Exploration function Takes a value estimate and a count, and returns an optimistic utility, e.g. (exact form not


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