Click to edit Master title style Batch RL Approximate...

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Approximate Models for Batch RL

Emma Brunskill

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Image from David Silver

FVI / FQI

Policy Iteration maintains both

an explicit representation of a policy and

the value of that policy

PI

Approximate model planners

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Forward Search w/Generative Model

Slide modified from David Silver

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Exact/Exhaustive Forward Search


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How many nodes in a H-depth tree (as a function of state space |S| and action space |A|)?


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How many nodes in a H-depth tree (as a function of state space |S| and action space |A|)? (|S||A|)H


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Sparse Sampling: Don’t Enumerate All Next States, Instead Sample Next States s’ ~ P(s’|s,a)

Sample n next states, si ~ P(s’|s,a)

Compute (1/n) Sumi V(s_i)

Converges to expected future reward: Sums’ p(s’|s,a)V(s’)


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Sparse Sampling: # nodes if sample n states at each action node? Independent of |S|! O(n|A|)H

Sample n next states, si ~ P(s’|s,a)

Compute (1/n) Sumi V(s_i)

Converges to expected future reward: Sums’ p(s’|s,a)V(s’)


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Sparse Sampling: # nodes if sample n states at each action node? Independent of |S|! O(n|A|)H

Upside: Can choose n to achieve bounds on the accuracy of the value function at the root state, independent of state space size

Downside: Still exponential in horizon, n still large for good bounds


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Limitation of Sparse Sampling

Slide modified from Alan Fern

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Monte Carlo Tree Search

Combine ideas of sparse sampling with an adaptive method for focusing on more promising parts of the ree

Here “more promising” means the actions that are seem likely to yield higher long term reward

Uses the idea of simulation search

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Simulation Based Search


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Simulation based Search


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Simple Monte Carlo Search


rollout policy dafa

greedy improvement with respect to fixed rollout policy

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Upper Confidence Tree (UCT)[Kocsis & Szepesvari, 2006]


• Combine forward search and simulation search• Instance of Monte-Carlo Tree Search

• Repeated Monte Carlo simulation of rollout policy• Rollouts add one or more nodes to search tree

• UCT• Uses optimism under uncertainty idea• Some nice theoretical properties

• Much better realtime performance than sparse sampling

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(Upper Confidence Bound)

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● Requires us to have a simulator/ generative model

● Each pass down the tree, follow tree policy until reach a state leaf where not all actions have been tried.

● Then need to simulate starting from that state leaf the result of taking another action

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Guarantees on UCT

Slide modified from Remi Munos

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Slide modified from slides from Alan Fern & David Silver

Computer GoPrevious game tree approaches faired poorly

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Rules of Go


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Position Evaluation in Go


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Monte Carlo Evaluation in Go:Planning problem, just a very very hard one


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Enormous Progress. MCTS Huge Impact


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Going Back to Batch RL...

• Use supervised learning method to compute model

• Use learned model with MCTS planning• Note: error in model will impact error in

estimated values!

• Computes an action for current state, take action, then redo planning for next state

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Autonomous Driving using Texplore (Hester and Stone 2013)

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Image from David Silver

FVI / FQI API

Approximate model planners

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