Provably Efficient Maximum Entropy Exploration

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Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as functions of the state-visitation frequencies that are induced by how the agent behaves. For example, one natural, intrinsically defined, objective problem is for the agent to learn a policy which induces a distribution over state space that is as uniform as possible, which can be measured in an entropic sense. We provide an efficient algorithm to optimize such such intrinsically defined objectives, when given access to a black box planning oracle (which is robust to function approximation). Furthermore, when restricted to the tabular setting where we have sample based access to the MDP, our proposed algorithm is provably efficient, both in terms of its sample and computational complexities. Key to our algorithmic methodology is utilizing the conditional gradient method (a.k.a. the Frank-Wolfe algorithm) which utilizes an approximate MDP solver.

Elad Hazan, Sham M. Kakade, Karan Singh, Abby Van Soest · 2018

Related benchmarks

Task	Dataset	Result
Transition model estimation	Pendulum discretized n = 10^5	Failure Rate0	8
Transition model estimation	Mountain Car discretized n = 10^6	Failure Count40	8
Reinforcement Learning	MuJoCo HalfCheetah Sparse v2 (test)	Max Average Return924.7	6
Reinforcement Learning	Delayed MuJoCo HalfCheetah v2 (test)	Average Return7907.98	6
Reinforcement Learning	Sparse MuJoCo Ant v2 (test)	Max Average Return940.7	6
Reinforcement Learning	Delayed MuJoCo Walker2d v2 (test)	Max Average Return4430.61	6
Reinforcement Learning	Sparse MuJoCo Walker2d v2 (test)	Max Return705.3	6
Reinforcement Learning	Delayed MuJoCo Hopper v2 (test)	Max Return3254.1	6
Reinforcement Learning	Sparse MuJoCo Hopper v2 (test)	Max Average Return879.5	6
Reinforcement Learning	Delayed MuJoCo Ant v2 (test)	Max Average Return1156.61	6