# CAPO: Constraint-Aware Prompt Optimization for LLM Agents

arXiv: https://arxiv.org/abs/2608.16068 · HTML: https://mlsanity.com/paper/2608.16068/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 36)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environment](https://mlsanity.com/paper/2506.07982/) (2025)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [RLPrompt: Optimizing Discrete Text Prompts with Reinforcement Learning](https://mlsanity.com/paper/2205.12548/) (2022)
- [SkillRL: Evolving Agents via Recursive Skill-Augmented Reinforcement Learning](https://mlsanity.com/paper/2602.08234/) (2026)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [OR-Bench: An Over-Refusal Benchmark for Large Language Models](https://mlsanity.com/paper/2405.20947/) (2024)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [Fast Lexically Constrained Decoding with Dynamic Beam Allocation for Neural Machine Translation](https://mlsanity.com/paper/1804.06609/) (2018)
- [NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraints](https://mlsanity.com/paper/2010.12884/) (2020)
- [Provably Efficient Safe Exploration via Primal-Dual Policy Optimization](https://mlsanity.com/paper/2003.00534/) (2020)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [EvoSkill: Automated Skill Discovery for Multi-Agent Systems](https://mlsanity.com/paper/2603.02766/) (2026)
- [Reinforcement Learning for Self-Improving Agent with Skill Library](https://mlsanity.com/paper/2512.17102/) (2025)
- [Controllable Natural Language Generation with Contrastive Prefixes](https://mlsanity.com/paper/2202.13257/) (2022)
- [InstructZero: Efficient Instruction Optimization for Black-Box Large Language Models](https://mlsanity.com/paper/2306.03082/) (2023)
- [SkillGrad: Optimizing Agent Skills Like Gradient Descent](https://mlsanity.com/paper/2605.27760/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly deployed as agents that rely on system prompts to use tools and complete tasks. Such deployments impose distinct operational requirements, including appropriate tool use, concise prompts and solution paths, and compliance with safety and formatting policies. For many practitioners, however, assembling domain-specific supervised data to post-train models to meet these requirements is infeasible. We introduce CAPO (Constraint-Aware Prompt Optimization), a primal-dual method that combines pool-based rewrites with adaptive constraint weighting to optimize system prompts under explicit operational constraints. Across agentic benchmarks, CAPO more reliably reaches empirically feasible operating points while improving task performance. CAPO also generalizes beyond agentic settings, achieving strong results on assistant-style evaluations with output-format and safety/privacy constraints. We further introduce DCAPO (Dynamically Trained CAPO), which trains a feedback- and dual-conditioned rewriter with pool-based GRPO while keeping the task agent frozen. Across task agents of different sizes, DCAPO produces a feasible prompt in every evaluated domain and matches or improves the task accuracy achieved by the evaluated baselines. A surrogate analysis characterizes how finite-pool and discrete-rewrite errors enter the inexact primal-dual procedure.