Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning (2407.15007v2)

Abstract: Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations, and has been widely applied to robotics, autonomous driving, and autoregressive text generation. The simplest approach to IL, behavior cloning (BC), is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner's access to the expert. We revisit the apparent gap between offline and online IL from a learning-theoretic perspective, with a focus on the realizable/well-specified setting with general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss, we show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. Specializing our results to deterministic, stationary policies, we show that the gap between offline and online IL is smaller than previously thought: (i) it is possible to achieve linear dependence on horizon in offline IL under dense rewards (matching what was previously only known to be achievable in online IL); and (ii) without further assumptions on the policy class, online IL cannot improve over offline IL with the logarithmic loss, even in benign MDPs. We complement our theoretical results with experiments on standard RL tasks and autoregressive language generation to validate the practical relevance of our findings.

Summary of "Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning"

The paper "Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning" by Dylan J. Foster, Adam Block, and Dipendra Misra investigates the impact of horizon on the sample complexity of offline and online imitation learning (IL) algorithms. The paper reevaluates the common belief that offline IL methods like Behavior Cloning (BC) inherently suffer from higher sample complexity due to a quadratic dependence on the horizon, compared to linear dependence achievable by online methods.

Main Contributions

The paper makes several key contributions to the understanding of sample complexity in IL:

1. Horizon-Independent Analysis of LogLossBC: Through a novel analysis of BC using the logarithmic loss (LogLossBC), the authors demonstrate that BC can achieve horizon-independent sample complexity under certain conditions. This is achieved whenever the range of cumulative payoffs is controlled and an appropriate notion of supervised learning complexity for the policy class is controlled.
2. Deterministic Policies: For deterministic, stationary policies and normalized rewards, the analysis shows that LogLossBC can achieve linear dependence on the horizon, challenging the traditional notion that offline IL is fundamentally harder than online IL.
3. Stochastic Policies: For stochastic expert policies, the paper establishes that while a purely $1/n$ rate (fast rate) is not achievable, the sample complexity can still be bounded in a variane-dependent manner, leading to tighter understanding of sample complexity in IL for general policy classes.
4. Gap Between Offline and Online IL: The paper concludes that the gap between offline and online IL is not fundamental under assumptions such as parameter sharing in policies. This is a notable shift from prior assumptions that online access is necessary to achieve favorable horizon dependence.
5. Empirical Validation: The theoretical findings are validated through experiments on standard reinforcement learning (RL) tasks and autoregressive language generation, supporting the practical relevance of the proposed theoretical constructs.

Theoretical Insights and Implications

The main theoretical insights revolve around the refined analysis of BC when applied with logarithmic loss, which directly challenges the perceived dichotomy between offline and online IL. By employing information-theoretic methods, the authors carefully dissect how different loss functions influence sample complexity bounds.

1. Supervised Learning Reduction: The analysis confirms that LogLossBC benefits from stronger generalization bounds due to its supervised learning perspective. This fundamentally allows BC to achieve horizon-independent or linear-in-horizon sample complexity in many cases.
2. Variance-Dependent Analysis: The paper also extends to stochastic experts, demonstrating that sample complexity can be analyzed in a problem-dependent manner. This suggests practical IL algorithms can be designed with variance-sensitive adaptations that close the gap between theoretical and empirical performance.
3. Optimality: The authors use lower bounds and constructive arguments to argue that their bounds on LogLossBC are tight. They specifically show that these bounds are near-optimal, even when compared against any online IL method, under general conditions.

Practical Implications

From a practical standpoint, the implications of this paper are significant for designing IL systems, especially in scenarios where assumptions regarding online access to the expert are relaxed.

1. Algorithm Design: The results suggest that practitioner focus might shift towards optimizing offline algorithms using more sophisticated loss functions like logarithmic loss, without necessarily resorting to more complex online interaction schemes.
2. Empirical Performance: The empirical validation across diverse tasks shows that the proposed theoretical frameworks translate well to practice, potentially guiding the implementation of more efficient IL algorithms.
3. Fine-Grained Understanding: By providing a detailed analysis of when and why horizon-independent performance can be achieved, the paper paves the way for a more nuanced approach to IL that eschews a one-size-fits-all framework.

Future Directions

The paper opens several avenues for future research:

1. Refining Horizon Effects: Further exploration into how specific structural properties of MDPs influence horizon dependence, potentially through control-theoretic perspectives.
2. Complexity Measures: Developing complexity measures that can quantitatively compare offline and online IL methods beyond horizon dependence.
3. Empirical Frameworks: Designing experimental frameworks that can rigorously test the theoretical findings across a broader range of IL tasks, especially ones involving sophisticated neural architectures and dynamic environments.
4. Robustness to Misspecification: Extending the analysis to misspecified policy classes, adding robustness to practical deployments where exact realizability cannot be guaranteed.

Conclusion

The paper provides a significant shift in understanding the sample complexity of imitation learning by showcasing that behavior cloning, when appropriately configured, can negate the purported disadvantages of offline algorithms in relation to the horizon. This bridges some gaps between theoretical and practical approaches in IL and instigates new discussions on the optimal design of IL algorithms. The comprehensive blend of theoretical insights and empirical validation makes this work a valuable resource for researchers and practitioners alike.