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From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling

🕒 Published (v1): 2026-04-28 16:53 UTC · Source: Arxiv · link

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Memory-enhanced LLM agents with decentralized debate for optimization modeling

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TL;DR

Agora-Opt is a modular agentic framework for LLM-based optimization modeling that couples decentralized multi-team debate with a read-write memory bank. Multiple agent teams independently produce solver-verified solutions and reach consensus through quantitative objective agreement rather than a moderator judge. The framework layers onto existing pipelines with minimal coupling, achieving the strongest overall performance across six public OR benchmarks.

Problem

Three compounding failures afflict current approaches to LLM-based optimization modeling: (1) base-LLM lock-in in training-centric methods (fine-tuned on Qwen2 cannot transfer to Qwen2.5 without re-tuning); (2) non-trainability in agentic methods, which use read-only RAG and cannot accumulate solver-verified experience after deployment; and (3) single-model myopia, where each reasoning step is handled by one backbone, limiting diversity and internal cross-checking.

Method

Agora-Opt instantiates two symmetric agent teams, each with a Formulator–Programmer–Debugger pipeline parametrized by a different backbone LLM \(\theta_A\) and \(\theta_B\). Given problem \(x\), each team independently produces a candidate solution \(s = (f, c, v, L)\) — formulation, solver code, objective value \(v \in \mathbb{R} \cup \{\perp\}\), and execution logs. The decentralized debate protocol compares objective values: agreement on \(v\) terminates debate and returns consensus; disagreement triggers iterative cross-team refinement guided by retrieved debate memory, with a stability-based fallback selection when a maximum round budget is exhausted. No centralized judge exists. The read-write memory bank stores two complementary stores: generation memory (verified formulation and debug patterns per task, retrieved during formulating and debugging stages) and debate memory (full reconciliation trajectories recording what each team proposed, which checks mattered, and which fixes converged), enabling training-free improvement between runs and across backbone upgrades.

Key Contributions

  • Agora-Opt framework: first coupling of decentralized debate with an agentic read-write memory bank for optimization modeling; modular, backbone-agnostic, stackable on existing pipelines.
  • Outcome-grounded debate protocol: consensus defined by solver-verified objective value alignment rather than a judge's subjective summary, enabling principled quantitative convergence and cross-backbone error repair.
  • Dual memory bank: generation memory (solution and debug memories) accelerates routine episodes; debate memory preserves consensus-building episodes so future debates start from richer verified experience.
  • OPT-Principled testbed: a curated benchmark of challenging OR instances complementing the six public benchmarks used for evaluation.
  • Backbone/method generality: demonstrated portability by instantiating teams with Gemini, GPT, and DeepSeek, and wrapping existing methods (ORLM, StepORLM, OptiMUS) inside the debate protocol.

Results

  • Agora-Opt achieves the strongest overall performance across all six public OR benchmarks compared against zero-shot LLMs, training-centric approaches (LLMOPT, ORLM, StepORLM), and prior agentic baselines (OptiMUS, ORMind).
  • Decentralized debate provides a structural advantage over centralized selection: it can recover correct formulations even when all initial candidate solutions are flawed, a regime where centralized judge selection cannot improve.
  • Memory retrieval provides incremental gains on top of debate alone (ablation results reported in Section 5, not fully reproduced in the provided excerpt).
  • Framework is robust across backbone swaps (Gemini, GPT, DeepSeek) and remains effective when wrapping ORLM, StepORLM, and OptiMUS as drop-in team implementations.

(Specific accuracy/solve-rate numbers are in tables not included in the provided excerpt.)

Limitations

  • The paper is truncated; stated limitations in Section 6 are not available.
  • Two agent teams running end-to-end plus iterative debate rounds multiplies inference cost relative to single-team methods.
  • Consensus rule (objective value alignment) is specific to optimization tasks with quantitative endpoints; the protocol does not generalize directly to open-ended generation tasks.
  • Memory quality depends on solver-verified episodes; if early runs produce systematically wrong formulations, debug and generation memories may encode incorrect patterns.
  • Maximum debate round budget introduces a hyperparameter sensitivity tradeoff between compute and solution quality (sensitivity analysis referenced but not reproduced here).

Relevance to Harnesses / Meta-Harnesses

Agora-Opt is architecturally a meta-harness: it wraps existing single-pipeline methods (ORLM, StepORLM, OptiMUS) as interchangeable team implementations and layers debate and memory coordination on top with minimal coupling — precisely the defining pattern of a meta-harness. Its read-write memory bank addresses a critical gap in harness design: accumulating solver-verified experience across runs and backbone upgrades without retraining, enabling the harness itself to improve over time. The decentralized debate protocol demonstrates a reusable orchestration primitive — consensus via objective signal rather than a moderator — applicable wherever harnesses wrap computationally verifiable outputs (solvers, test suites, compilers). The backbone-agnostic modularity and explicit resistance to base-model lock-in are directly transferable design principles for anyone building harnesses that must outlive specific model releases.