Split the Differences, Pool the Rest: Provably Efficient Multi-Objective Imitation

TL;DR

This paper introduces MA-BC, a provably efficient algorithm for multi-objective imitation learning that effectively combines expert data to recover Pareto-optimal policies, supported by theoretical guarantees and empirical validation.

Contribution

The paper proposes MA-BC, a novel algorithm with proven convergence and optimality properties for multi-objective imitation learning, addressing limitations of existing methods.

Findings

MA-BC converges faster to Pareto-optimal policies than independent learners.

MA-BC is minimax optimal for multi-objective imitation.

Empirical results validate MA-BC across diverse environments.

Abstract

This work investigates multi-objective imitation learning: the problem of recovering policies that lie on the Pareto front given demonstrations from multiple Pareto-optimal experts in a Multi-Objective Markov Decision Process (MOMDP). Standard imitation approaches are ill-equipped for this regime, as naively aggregating conflicting expert trajectories can result in dominated policies. To address this, we introduce Multi-Output Augmented Behavioral Cloning (MA-BC), an algorithm that systematically partitions divergent expert data while pooling state-action pairs where no behavior conflict is observed. Theoretically, we prove that MA-BC converges to Pareto-optimal policies at a faster statistical rate than any learner that considers each expert dataset independently. Furthermore, we establish a novel lower bound for multi-objective imitation learning, demonstrating that MA-BC is minimax optimal. Finally, we empirically validate our algorithm across diverse discrete environments and, guided by our theoretical insights, extend and evaluate MA-BC on a continuous Linear Quadratic Regulator (LQR) control task.