A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning (1011.0686v3)

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.

• The paper's main contribution is the DAgger algorithm that iteratively aggregates data and guarantees no-regret performance while reducing imitation learning errors.
• It leverages a reduction to no-regret online learning, ensuring error growth scales linearly with task horizon and classification error.
• Experimental results validate DAgger's superior performance in real-world tasks like car steering, video games, and handwriting recognition.

A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning

The paper "A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning" by Stéphane Ross, Geoffrey J. Gordon, and J. Andrew Bagnell presents significant advancements in the domain of sequential prediction problems, specifically addressing challenges in imitation learning. The authors propose a novel iterative algorithm, DAgger (Dataset Aggregation), which mitigates the limitations of previous methods by training a stationary deterministic policy capable of performing well under its induced distribution of states.

Background and Motivation

Sequential prediction problems, such as those found in imitation learning, pose unique challenges because future observations in these settings depend on previous predictions or actions. This dependency violates the independent and identically distributed (i.i.d.) assumptions commonly made in statistical learning, resulting in suboptimal performance in both theoretical and practical scenarios. Traditional approaches to imitation learning, which train classifiers or regressors to predict expert behavior, often fail because the predictions (actions) made by the learner change the distribution of future inputs in a way that compounds errors.

Recent methods have attempted to address these issues, either by training non-stationary policies or by employing specific iterative techniques. However, these methods often require a large number of iterations or result in stochastic policies that can be unsatisfactory for practical applications.

Contributions

The main contributions of this paper are as follows:

1. DAgger Algorithm: The authors introduce DAgger, an iterative meta-algorithm that learns a deterministic policy through a reduction-based approach. DAgger leverages existing supervised learning techniques and operates as a no-regret online learning algorithm. It constructs an aggregate dataset over iterations by collecting training data under the current policy and continually updating the policy to minimize errors.
2. Performance Guarantees: The paper provides theoretical analysis and guarantees for the DAgger method, showing that the algorithm can achieve expected performance where the number of mistakes scales linearly with the task horizon $T$ and classification error $\epsilon$. This significantly improves upon traditional supervised learning methods, which suffer from quadratic growth in errors relative to $T$.
3. Experimental Validation: The authors demonstrate DAgger's efficacy and scalability on several challenging imitation learning problems, including learning to steer a car in the Super Tux Kart racing game and playing Super Mario Bros. They also apply DAgger to handwriting recognition as a structured prediction problem, showcasing its competitive performance against state-of-the-art methods.

Technical Summary

The DAgger algorithm iteratively gathers data using the current policy and aggregates this data to train an improved policy at each iteration. At the initial iteration, the policy corresponds to the expert's policy, ensuring a grounded starting point. Subsequent iterations involve mixing the learned policy with the expert's policy to collect diverse training data. This data aggregation guarantees that the policy is trained on distributions it will encounter during execution, rather than relying solely on the expert's demonstrations.

The authors underscore that any no-regret learning algorithm can be applied in this setting, provided it treats mini-batches of trajectory data as individual online learning examples. The use of strongly convex loss functions in the analysis further ensures robust performance guarantees under the DAgger framework.

Experimental Results

Key numerical results from the experiments include:

• Super Tux Kart: DAgger outperformed baseline supervised learning and SMILe, achieving a policy that never falls off the track after sufficient iterations.
• Super Mario Bros.: DAgger resulted in significantly higher scores compared to traditional supervised learning and competitor algorithms like SMILe and SEARN.
• Handwriting Recognition: DAgger achieved 85.5% character accuracy, surpassing both the supervised approach and other structured prediction methodologies.

Implications and Future Work

The theoretical and practical innovations presented in this paper have broad implications for the fields of imitation learning and structured prediction. By reducing these complex sequential prediction problems to no-regret online learning, the authors provide a robust and scalable framework that can be adapted to various applications beyond the specific problems addressed.

Future work could explore more sophisticated strategies for structured prediction, such as multi-pass and beam-search decoding. Additionally, integrating Inverse Optimal Control techniques could further enhance policy performance in imitation learning settings. Extending these methods to reinforcement learning scenarios, where the cost-to-go must be estimated, remains a promising direction for further research.

In conclusion, the paper's contributions to reducing imitation learning and structured prediction to no-regret online learning represent a significant step forward in the development of reliable, efficient, and theoretically sound algorithms for sequential decision-making tasks.