Adaptive Incentive Design for Markov Decision Processes with Unknown Rewards
Abstract: Incentive design, also known as model design or environment design for Markov decision processes(MDPs), refers to a class of problems in which a leader can incentivize his follower by modifying the follower's reward function, in anticipation that the follower's optimal policy in the resulting MDP can be desirable for the leader's objective. In this work, we propose gradient-ascent algorithms to compute the leader's optimal incentive design, despite the lack of knowledge about the follower's reward function.
First, we formulate the incentive design problem as a bi-level optimization {problem} and demonstrate that, by the softmax temporal consistency between the follower's policy and value function, the bi-level optimization {problem} can be reduced to single-level optimization, for which a gradient-based algorithm can be developed to optimize the leader's objective. We establish several key properties of incentive design in MDPs and prove the convergence of the proposed gradient-based method.
Next, we show that the gradient terms can be estimated from observations of the follower's best response policy, enabling the use of a stochastic gradient-ascent algorithm to compute a locally optimal incentive design without knowing or learning the follower's reward function.
Finally, we analyze the conditions under which an incentive design remains optimal for two different rewards which are policy invariant.
The effectiveness of the proposed algorithm is demonstrated using a small probabilistic transition system and a stochastic gridworld.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Pascal_Poupart2
Submission Number: 3304
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