AlgoSkill: Learning to Design Algorithms by Scheduling Human-Like Skills

2026-06-29

AI Summary

This work proposes a novel paradigm for automatically synthesizing efficient and correct algorithms from natural language problem descriptions, eschewing direct code generation. The approach models algorithm design as a sequential decision process over a typed library of algorithmic skills, where a learned scheduler selects appropriate skills guided by Monte Carlo Tree Search (MCTS) and multilevel verification feedback—including compilation, test execution, complexity analysis, and adversarial stress testing. The key innovation lies in decomposing algorithm design into human-like, schedulable skill units and introducing a verification-guided skill scheduling mechanism. Experiments demonstrate that the method substantially outperforms strong baselines—including end-to-end generation, chain-of-thought prompting, self-improvement approaches, and skill-agnostic MCTS—on competitive programming and combinatorial optimization benchmarks, with ablation studies confirming the contribution of each component.

Abstract

Designing an algorithm from a natural-language problem statement requires identifying the problem structure, reading constraints, choosing a suitable paradigm, checking correctness, and refining complexity. Existing large language model (LLM) methods often rely on direct generation or generic self-refinement, leaving these steps implicit. We propose AlgoSkill, which models algorithm design as sequential decision-making over a typed library of algorithmic skills, including abstraction, constraint analysis, state design, data-structure selection, proof checking, counterexample construction, and complexity refinement. A learned scheduler proposes skills from the current design state, while a Monte Carlo Tree Search (MCTS) controller explores skill sequences using verification feedback from compilation, testing, stress testing, and complexity analysis. Experiments on competitive programming and combinatorial optimization benchmarks show that AlgoSkill improves over direct LLM generation, chain-of-thought prompting, self-refinement, and MCTS without typed skills. Ablations show that typed skills, verification-based repair, and search-based scheduling each contribute to performance. These results support treating automatic algorithm design as verification-guided skill scheduling rather than one-shot code generation.

Problem

• algorithm design
• large language models
• automatic programming
• skill scheduling
• verification-guided generation

Innovation

• algorithm design
• skill scheduling
• Monte Carlo Tree Search
• verification-guided learning
• typed skill library