Greedy Is Enough: Sparse Action Discovery in Agentic LLMs

TL;DR

This paper demonstrates that in large action spaces, only a small subset of actions are relevant, and a greedy algorithm can efficiently identify these actions with high probability, providing a theoretical basis for action pruning in agentic systems.

Contribution

It introduces a formal framework for sparse action discovery using a block-sparse recovery approach and proves the effectiveness of a greedy algorithm under standard assumptions.

Findings

Greedy algorithm recovers relevant actions with high probability.

Sample complexity scales polynomially with sparsity and latent dimension.

Sparsity and coverage are necessary for tractable action discovery.

Abstract

Modern agentic systems operate in environments with extremely large action spaces, such as tool-augmented language models with thousands of available APIs or retrieval operations. Despite this scale, empirical evidence suggests that only a small subset of actions meaningfully influences performance in a given deployment. Motivated by this observation, we study a contextual linear reward model in which action relevance is governed by a structured sparsity assumption: only a small number of actions have nonzero effects across latent states. We formulate action discovery as a block-sparse recovery problem and analyze a greedy algorithm inspired by Orthogonal Matching Pursuit. Under standard assumptions on incoherence, signal strength, and action coverage, we prove that the greedy procedure exactly recovers the relevant action set with high probability, using a number of samples that scales polynomially in the sparsity level and latent dimension, and only logarithmically in the total number of actions. We further provide estimation error guarantees for refitted parameters and show that the resulting decision rule is near-optimal for new latent states. Complementing these results, we establish information-theoretic lower bounds demonstrating that sparsity and sufficient coverage are necessary for tractability. Together, our results identify sparse action discovery as a fundamental principle underlying large-action decision-making and provide a theoretical foundation for action pruning in agentic systems.