Large language models (LLMs) have demonstrated remarkable reasoning and planning capabilities, driving extensive research into task decomposition.Existing task decomposition methods focus primarily on memory, tool usage, and feedback mechanisms, achieving notable success in specific domains, but they often overlook the trade-off between performance and cost.In this study, we first conduct a comprehensive investigation on task decomposition, identifying six categorization schemes.Then, we perform an empirical analysis of three factors that influence the performance and cost of task decomposition: categories of approaches, characteristics of tasks, and configuration of decomposition and execution models, uncovering three critical insights and summarizing a set of practical principles.Building on this analysis, we propose the Select-Then-Decompose strategy, which establishes a closed-loop problemsolving process composed of three stages: selection, execution, and verification.This strategy dynamically selects the most suitable decomposition approach based on task characteristics and enhances the reliability of the results through a verification module.Comprehensive evaluations across multiple benchmarks show that the Select-Then-Decompose consistently lies on the Pareto frontier, demonstrating an optimal balance between performance and cost.Our code is publicly available at https://github.com/summervvind/ Select-Then-Decompose.

Policy space response oracle (PSRO) is a population-based algorithm that can be used to solve two-player zero-sum games. In the PSRO solution framework, optimizing policy diversity is crucial for addressing nontransitive game problems, helping the agent population avoid exploitation by unfamiliar opponents. In addition, while deep reinforcement learning is highly effective in solving complex game environments, its integration with PSRO remains fragmented and lacking in effective coordination. In this study, we propose distributed PSRO to efficiently solve complex game scenarios. To enhance diversity while managing optimization costs, we introduce TOP-K truncation, which prioritizes high-quality opponents and limits the size of the policy pool during sampling. This approach not only reduces interference from less effective strategies but also ensures computational efficiency by seamlessly integrating with our distributed training framework. We also design the distributed training framework to incorporate diversity estimation directly into the sampling process, achieving diversity optimization without incurring additional computational overhead. Furthermore, we introduce the opponent first (OF) method, which enhances decision-making by leveraging opponent information during interaction sampling. We perform experimental validation using a nontransitive mixture model and AlphaStar888 to confirm the effectiveness of the TOP-K truncation approach. Finally, we demonstrate the feasibility and efficiency of the distributed training framework and the OF approach in a Google Research Football 11 versus 11 scenario.