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EARL-BO: Reinforcement Learning for Multi-Step Lookahead, High-Dimensional Bayesian Optimization

Published 31 Oct 2024 in cs.LG and math.OC | (2411.00171v1)

Abstract: Conventional methods for Bayesian optimization (BO) primarily involve one-step optimal decisions (e.g., maximizing expected improvement of the next step). To avoid myopic behavior, multi-step lookahead BO algorithms such as rollout strategies consider the sequential decision-making nature of BO, i.e., as a stochastic dynamic programming (SDP) problem, demonstrating promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues, e.g., being limited to two-step lookahead. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the SDP of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and employ off-policy learning to accelerate its initial training. We then propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for Bayesian Optimization), on both synthetic benchmark functions and real-world hyperparameter optimization problems, demonstrating significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.

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Summary

  • The paper introduces EARL-BO, a framework that integrates reinforcement learning with Bayesian optimization to enable efficient multi-step lookahead in high-dimensional spaces.
  • It utilizes an Attention-DeepSets encoder to manage large state spaces and employs off-policy learning via a GP virtual environment for robust decision-making.
  • Evaluation on synthetic and hyperparameter optimization benchmarks shows EARL-BO's competitive performance, advancing multi-step planning methods beyond traditional approaches.

Reinforcement Learning for Advanced Bayesian Optimization Strategies

The paper "EARL-BO: Reinforcement Learning for Multi-Step Lookahead, High-Dimensional Bayesian Optimization" introduces a novel framework that leverages reinforcement learning (RL) to address the challenges of multi-step lookahead in Bayesian Optimization (BO), particularly in high-dimensional settings. This approach, termed EARL-BO (Encoder Augmented RL for Bayesian Optimization), is designed to improve the scalability and efficiency of BO by overcoming the scalability issues faced by traditional multi-step methods.

Core Contributions

The paper makes several significant contributions to the field of Bayesian Optimization:

  • Integration of RL with BO: The authors propose using reinforcement learning, specifically Proximal Policy Optimization (PPO), to improve decision-making quality in BO by formulating it as a stochastic dynamic programming problem. This approach enables efficient multi-step lookahead, which considers the sequential decision-making nature of BO rather than the prevalent one-step lookahead strategies.
  • Attention-DeepSets Encoder: To efficiently encode the state space in high-dimensional settings, the approach utilizes an Attention-DeepSets architecture. This permits permutation and size invariance, crucial for representing BO data while enabling the model to focus on more relevant points through attention mechanisms.
  • Off-policy Learning and GP Virtual Environment: The framework employs off-policy learning using samples from the TuRBO algorithm to initially train the RL agent, which accelerates convergence and improves robustness. Moreover, the use of a GP-based virtual environment allows exploration and learning without the overhead of costly real-world evaluations.

Methodological Insights

This research introduces a sophisticated interaction between BO and RL. The study acknowledges the inherent challenges in multi-step lookahead, such as computational complexity and approximation errors in high-dimensional spaces, and addresses these issues with a tailored RL approach. By using attention mechanisms with DeepSets, the encoder efficiently processes large datasets, facilitating state representation in a manner that maintains actionability across varying problem scales.

EARL-BO exploits the strengths of RL in handling dynamic environments and integrates it into the inherently sequential nature of BO. The paper details a procedural approach where the RL agent's interaction with a GP-derived model allows a simulated exploration of the optimization landscape, thus determining effective multi-step acquisition strategies. Consequently, the RL agent benefits from scalable, robust training dynamics, inherently balancing exploration and exploitation over the decision horizon.

Evaluation and Results

The evaluation presents both synthetic benchmarks and practical hyperparameter optimization tasks. In synthetic benchmarks, EARL-BO demonstrates competitive performance against existing methods, outperforming baseline methods, particularly in higher-dimensional scenarios. The results reflect the advantage of multi-step planning intrinsic to EARL-BO, which remains robust across different function aspects and scales.

In hyperparameter optimization benchmarks, EARL-BO consistently excels, asserting the benefits gained from the proposed methodology in realistic tasks. The study reveals that even with limited initial samples, EARL-BO adapts effectively, outperforming standard single-step lookahead methods, thus confirming the hypothesis of enhanced decision-making capabilities facilitated by multi-step lookahead.

Implications and Future Directions

The implications of this research are profound for the practical deployment of BO methods in high-dimensional and costly evaluation contexts. By demonstrating the utility of RL in optimizing long-term reward accumulation, the EARL-BO framework offers a new paradigm in the field. It moves beyond the limitations of traditional acquisition functions and introduces a method to directly account for the sequential nature of decisions in BO.

Future research can explore further integration of more complex RL architectures, perhaps using transformer-based models for an even richer representation of the state spaces. Additionally, further experimentation on varying types of surrogate models beyond GPs could yield insights into more general adaptable frameworks that address the curse of dimensionality and variability issues faced in meta-learning tasks. The research opens pathways for deploying such techniques in an array of scenarios, from autonomous experimentation systems to design in materials science, where decision impact optimization is crucial.

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