[Paper Review] Provable Representation Learning for Imitation Learning via Bi-level Optimization

Sanjeev Arora, Simon S. Du+3 more|arXiv (Cornell University)|Feb 24, 2020

Reinforcement Learning in Robotics37 references4 citations

TL;DR

This paper proposes a bi-level optimization framework for provable representation learning in imitation learning, where a shared representation is learned from multiple expert trajectories to reduce sample complexity. The method achieves theoretical guarantees in both behavior cloning and observation-alone settings, demonstrating that representation learning can significantly improve sample efficiency in imitation learning tasks.

ABSTRACT

A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts' trajectories are available. We formulate representation learning as a bi-level optimization problem where the "outer" optimization tries to learn the joint representation and the "inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters. We instantiate this framework for the imitation learning settings of behavior cloning and observation-alone. Theoretically, we show using our framework that representation learning can provide sample complexity benefits for imitation learning in both settings. We also provide proof-of-concept experiments to verify our theory.

Motivation & Objective

• To address the high sample complexity in imitation learning by leveraging representation learning from multiple expert demonstrations.
• To formalize representation learning in imitation learning as a bi-level optimization problem, separating joint representation learning from task-specific policy learning.
• To provide provable sample complexity benefits for imitation learning in both settings where expert actions are observable (behavior cloning) and unobservable (observation-alone).
• To empirically validate the theoretical insights through experiments in environments like NoisyCombinationLock and SwimmerVelocity.
• To bridge multi-task representation learning in supervised learning with single-task imitation learning, offering non-convex loss guarantees.

Proposed method

• Formulate imitation learning as a bi-level optimization: the outer level learns a shared representation, and the inner level learns task-specific policies via imitation.
• For behavior cloning, the inner optimization minimizes cross-entropy between expert actions and policy outputs, using a shared representation.
• For the observation-alone setting, the inner optimization uses a min-max formulation inspired by Sun et al. (2019), enabling interaction with the environment to infer policies.
• The framework allows the agent to interact with the environment in the observation-alone setting, enabling policy learning without access to expert actions.
• The representation is parameterized by a neural network (e.g., ReLU-activated linear layer), jointly optimized with task-specific heads via end-to-end training.
• The overall loss combines behavior cloning objectives across all tasks, minimizing the negative log-likelihood of expert actions under the policy conditioned on the shared representation.

Experimental results

Research questions

• RQ1 Can representation learning provably reduce sample complexity in imitation learning when multiple experts demonstrate different MDPs?
• RQ2 Does the bi-level optimization framework enable effective representation learning in the behavior cloning setting where expert actions are available?
• RQ3 Can the framework generalize to the more challenging observation-alone setting where expert actions are hidden?
• RQ4 What is the theoretical sample complexity benefit of using a shared representation compared to learning from scratch?
• RQ5 How does the framework perform empirically in reducing sample requirements for policy learning in complex environments?

Key findings

• The proposed bi-level optimization framework provides provable sample complexity benefits in both behavior cloning and observation-alone imitation learning settings.
• In behavior cloning, the framework shows that with sufficient experts, the representation reduces the number of demonstrations needed for a new task.
• In the observation-alone setting, the min-max inner optimization enables policy learning without expert action supervision, with theoretical guarantees on sample efficiency.
• Experiments on NoisyCombinationLock and SwimmerVelocity demonstrate that representation learning enables faster policy convergence with fewer demonstrations.
• Policy optimization using the learned representation achieves higher returns with fewer training steps compared to training from random initialization.
• The framework successfully generalizes across tasks, showing that representations learned from diverse experts improve zero-shot transfer to new imitation learning tasks.