[Paper Review] A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning

Stéphane Ross, Geoffrey J. Gordon+1 more|arXiv (Cornell University)|Nov 2, 2010

Advanced Bandit Algorithms ResearchDecision Sciences840 citations

TL;DR

This paper proposes DAGGER, a novel iterative algorithm that reduces imitation learning and structured prediction to no-regret online learning, enabling the training of stationary deterministic policies with strong theoretical guarantees. By iteratively collecting expert demonstrations on states induced by the current policy, DAGGER ensures linear growth in error over time, outperforming prior methods like SMILe and SEARN in both imitation learning and sequence labeling tasks with improved stability and sample efficiency.

ABSTRACT

Sequential prediction problems such as imitation learning, where future observations depend on previous predictions (actions), violate the common i.i.d. assumptions made in statistical learning. This leads to poor performance in theory and often in practice. Some recent approaches provide stronger guarantees in this setting, but remain somewhat unsatisfactory as they train either non-stationary or stochastic policies and require a large number of iterations. In this paper, we propose a new iterative algorithm, which trains a stationary deterministic policy, that can be seen as a no regret algorithm in an online learning setting. We show that any such no regret algorithm, combined with additional reduction assumptions, must find a policy with good performance under the distribution of observations it induces in such sequential settings. We demonstrate that this new approach outperforms previous approaches on two challenging imitation learning problems and a benchmark sequence labeling problem.

Motivation & Objective

• To address the distribution shift problem in imitation learning, where standard i.i.d. supervised learning fails due to policy-induced state distribution changes.
• To develop a method that trains stationary deterministic policies with strong theoretical guarantees on performance under the induced state distribution.
• To reduce imitation learning and structured prediction to online no-regret learning, enabling reuse of standard supervised learning algorithms.
• To improve sample efficiency and stability over prior iterative methods like SMILe and SEARN, which use stochastic or non-stationary policies.
• To demonstrate the approach on challenging real-world tasks, including robotic control and handwriting recognition, with competitive results.

Proposed method

• Proposes DAGGER, an iterative algorithm that collects expert demonstrations on states induced by the current policy, forming a growing dataset for supervised learning.
• Uses a no-regret online learning framework, where each iteration improves the policy by minimizing regret over the accumulated dataset.
• Employs a reduction-based approach (Beygelzimer et al., 2005) to transform imitation learning into a no-regret learning problem, ensuring theoretical performance bounds.
• Applies online-to-batch techniques to analyze sample complexity and ensure convergence with finite data.
• Uses a weighted combination of past policies and expert data, with decay factors (e.g., βi = 0.5^{i-1}) to prioritize recent and relevant data.
• Adapts the method to structured prediction by treating sequential prediction as a degenerate imitation learning problem with deterministic dynamics.

Experimental results

Research questions

• RQ1 Can a no-regret online learning framework be effectively applied to imitation learning to ensure linear error growth under policy-induced distributions?
• RQ2 How can a stationary deterministic policy be trained with strong theoretical guarantees in sequential decision-making under distribution shift?
• RQ3 What is the impact of data collection strategy on policy performance and sample efficiency in iterative imitation learning?
• RQ4 How does DAGGER compare to existing iterative methods like SMILe and SEARN in terms of stability, convergence, and final performance?
• RQ5 Can the reduction to no-regret learning be extended to structured prediction tasks with sequential dependencies?

Key findings

• DAGGER outperforms the supervised baseline on the Super Mario Bros. task, achieving 3030 points compared to 2980 with the indicator function and 2800 with the supervised approach.
• On the Super Tux Kart racing task, DAGGER significantly outperforms all other methods, including SMILe and SEARN, with a clear convergence trend over iterations.
• In the OCR benchmark, DAGGER achieves 85.5% character accuracy, surpassing the supervised baseline (83.6%) and outperforming SEARN with α=0.1 and SMILe.
• The method achieves linear growth in total cost (J(π)) with respect to task horizon T and classification error ϵ, matching theoretical guarantees from no-regret learning.
• DAGGER demonstrates improved stability and sample efficiency, avoiding the instability of stochastic mixtures used in SMILe and the performance stagnation of supervised learning.
• The use of decayed weighting (βi = 0.5^{i-1}) leads to better data diversity and performance than uniform or indicator-based weighting, especially in early iterations.