Maximum Entropy Differential Dynamic Programming

TL;DR

This paper introduces a maximum entropy-based extension of Differential Dynamic Programming that enables better exploration of complex cost landscapes with multiple local minima, improving solution quality.

Contribution

It proposes a novel maximum entropy formulation for DDP with unimodal and multimodal value functions, allowing escape from local minima through exploration.

Findings

Outperforms vanilla DDP on multi-minima tasks

Enables exploration with multimodal policies

Connects with linearly solvable stochastic control

Abstract

In this paper, we present a novel maximum entropy formulation of the Differential Dynamic Programming algorithm and derive two variants using unimodal and multimodal value functions parameterizations. By combining the maximum entropy Bellman equations with a particular approximation of the cost function, we are able to obtain a new formulation of Differential Dynamic Programming which is able to escape from local minima via exploration with a multimodal policy. To demonstrate the efficacy of the proposed algorithm, we provide experimental results using four systems on tasks that are represented by cost functions with multiple local minima and compare them against vanilla Differential Dynamic Programming. Furthermore, we discuss connections with previous work on the linearly solvable stochastic control framework and its extensions in relation to compositionality.