[Paper Review] Reinforcement and Imitation Learning via Interactive No-Regret Learning

Stéphane Ross, J. Andrew Bagnell|arXiv (Cornell University)|Jun 23, 2014

Advanced Bandit Algorithms Research23 references118 citations

TL;DR

This paper introduces AggreVaTe, a no-regret online learning framework that unifies imitation and reinforcement learning by incorporating cost-to-go information into interactive policy learning. It extends DAgger-style methods with cost-sensitive learning, enabling stronger theoretical guarantees and improved policy stability through regret minimization, with applications to both imitation and approximate policy iteration.

ABSTRACT

Recent work has demonstrated that problems-- particularly imitation learning and structured prediction-- where a learner's predictions influence the input-distribution it is tested on can be naturally addressed by an interactive approach and analyzed using no-regret online learning. These approaches to imitation learning, however, neither require nor benefit from information about the cost of actions. We extend existing results in two directions: first, we develop an interactive imitation learning approach that leverages cost information; second, we extend the technique to address reinforcement learning. The results provide theoretical support to the commonly observed successes of online approximate policy iteration. Our approach suggests a broad new family of algorithms and provides a unifying view of existing techniques for imitation and reinforcement learning.

Motivation & Objective

• Address the limitation of existing imitation learning methods that ignore cost-to-go information, leading to suboptimal policies in high-cost scenarios (e.g., driving off a cliff).
• Provide a theoretical foundation for the empirical success of online approximate policy iteration, which often outperforms batch methods despite lacking formal convergence guarantees.
• Unify existing techniques in imitation and reinforcement learning under a single no-regret learning framework that leverages cost-sensitive feedback.
• Develop a new algorithm, NRPI (No-Regret Policy Iteration), for reinforcement learning with strong theoretical stability and performance guarantees.
• Demonstrate that cost-to-go estimates, even crudely approximated, can significantly improve policy generalization and robustness in interactive learning settings.

Proposed method

• Propose AggreVaTe, an interactive imitation learning algorithm that collects cost-weighted training examples $(s, t, a, Q)$, where $Q$ is the expert’s cost-to-go after taking action $a$ in state $s$ at time $t$.
• Train a policy $ ilde{ au}$ to minimize expected cost-to-go on the collected dataset, rather than minimizing zero-one classification loss on expert actions.
• Use online no-regret learning algorithms (e.g., online Frank-Wolfe) to iteratively improve the policy, ensuring that cumulative regret grows sublinearly over time.
• Extend the framework to reinforcement learning by introducing NRPI, a no-regret policy iteration algorithm that uses the same cost-sensitive learning mechanism to ensure stability and performance guarantees.
• Leverage time-averaged state distributions $d_ au^t$ and cost functions $C(s,a) \in [0,1]$ to define performance metrics and regret bounds.
• Establish theoretical bounds showing that the algorithm achieves statistical regret rather than error reduction, providing stronger performance guarantees than traditional methods.

Experimental results

Research questions

• RQ1 Can incorporating cost-to-go information into interactive imitation learning improve policy performance and robustness compared to methods that only mimic expert actions?
• RQ2 Why do online approximate policy iteration methods often perform better in practice than batch methods, despite theoretical instability concerns?
• RQ3 Can a unifying framework based on no-regret online learning be constructed to encompass both imitation learning and reinforcement learning?
• RQ4 How can cost-sensitive no-regret learning be used to derive stable and theoretically grounded reinforcement learning algorithms?
• RQ5 What are the practical implications of using multiple past policies in training, rather than just the most recent one, for improving convergence and stability?

Key findings

• AggreVaTe achieves a statistical regret bound that is stronger than error reduction guarantees, providing a more robust theoretical foundation for interactive imitation learning.
• The method demonstrates that using cost-to-go estimates—such as those from expert rollouts or heuristics—can prevent the learning of dangerous or high-cost policies, even when expert actions are ambiguous.
• NRPI, the extension to reinforcement learning, provides theoretical guarantees comparable to the strongest existing results in the literature, with performance bounded in terms of regret over time.
• Theoretical analysis shows that if exploration distributions $ u_{1:T}$ converge to the state distribution of an optimal policy, AggreVaTe is guaranteed to converge to an optimal policy in $ ilde{ au}$.
• Empirical results suggest that training on multiple past policies (not just the most recent) reduces oscillations and divergence, improving stability in approximate dynamic programming.
• The framework explains the success of heuristic methods like SEARN, which use expert rollouts as cost-to-go estimates, as a special case of AggreVaTe using online Frank-Wolfe.