AlgoSkill: Learning to Design Algorithms by Scheduling Human-Like Skills
For researchers and practitioners using LLMs for algorithm design, AlgoSkill provides a structured approach that outperforms existing methods, though the gains are incremental over strong baselines.
AlgoSkill models algorithm design as sequential decision-making over typed skills, improving success rates on competitive programming and combinatorial optimization benchmarks over direct LLM generation, chain-of-thought, self-refinement, and MCTS without typed skills.
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.