Learning to Harvest Without Collapse in a Regenerative Commons: A Lagrangian Framework

Jose Tupayachi; Xueping Li; Soham Das

Home/Archive/arXiv

arXiv · 2609.36478

Learning to Harvest Without Collapse in a Regenerative Commons: A Lagrangian Framework

Jose Tupayachi·Xueping Li·Soham Das

View original source ↗Read source document ↗Export metadata ↓

Abstract

The tragedy of the commons poses a multi-agent safety problem: reward-seeking agents can deplete a shared resource, and cooperation among its users does not itself specify how much must be preserved. We make preservation an explicit requirement by formulating a regenerative commons as a constrained Markov game or a constrained multi-agent MDP with a designer-specified depletion budget. We develop a nonstationary Lagrangian framework that constructs a policy sequence from solutions of unconstrained games or cooperative control problems. Extending earlier time-average constructions, we introduce average-epoch solution concepts for reset episodes with discounted rewards and terminal costs. We prove a reward-independent feasibility certificate, cooperative feasibility and approximate optimality against feasible policy mixtures, and an extension to unbiased sampled costs. For self-interested agents, a constrained Nash certificate quantifies the price-dispersion term introduced by deviations that redistribute budget across epochs. Under the stated assumptions on solver accuracy and multiplier updates, these results give constrained policy-sequence guarantees using solutions of unconstrained problems. Experiments with constrained IPPO and MAPPO in a Gordon-Schaefer fishery examine how depletion budgets shape stock retention, harvest rewards, and price adaptation.

Explore related subjects

cs.AI cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Jose Tupayachi, Xueping Li, Soham Das. 2026-09-29. Learning to Harvest Without Collapse in a Regenerative Commons: A Lagrangian Framework. https://arxiv.org/abs/2609.36478

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Evaluating Test-Time Scaling of General LLM Agents

LLM agents are increasingly expected to operate as general-purpose systems that resolve real-world user requests, yet their dynamic scaling behavior in realistic environments remains poorly understood. In this paper, we systematically investigate two principal test-time scaling axes of LLM agents: sequential scaling through extended interaction and parallel scaling through trajectory sampling. We first introduce a realistic benchmark that provides one unified framework for evaluating LLM agents across search, coding, reasoning, and tool-use domains, more faithfully reflecting the heterogeneity of real-world deployments. Evaluating ten leading LLM agents reveals substantial performance degradation when transitioning from domain-specific evaluations to this realistic setting. Building on this foundation, we progressively scale test-time compute along fine-grained increments to characterize the performance upper bound. We find that neither scaling axis can consistently yield meaningful gains from additional test-time compute in realistic environments, a phenomenon we attribute to two fundamental limitations: the scaling plateau that bottlenecks sequential scaling and the verification gap that undermines parallel scaling. Code is publicly available at https://github.com/cxcscmu/General-AgentBench.

cs.AI↗

arXiv2026

EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibrium

Multi-agent debate (MAD) systems increasingly rely on shared memory to support long-horizon reasoning, but this convenience opens a critical vulnerability: a single corrupted entry can contaminate the downstream memory-augmented reasoning, and debate alone fails to filter such errors. Existing safeguards filter entries via heuristics or LLM-based validation, yet they rely on AI judgments that share the same failure modes and overlook the cross-agent dynamics of MAD. We address this gap by formulating memory updating in MAD as a zero-trust memory game, in which no agent is assumed reliable and the game's equilibrium motivates a principled objective for calibrating memory influence. Guided by this objective, we propose EquiMem, an inference-time calibration mechanism that evaluates each update against the shared memory state and the memory already being used by other agents, using their existing retrieval queries and traversal paths as evidence of calibration. EquiMem instantiates this calibration for both embedding- and graph-based memory, and across diverse benchmarks, MAD frameworks, and memory architectures, it consistently outperforms existing safeguards, remains robust under adversarial agents, and incurs negligible inference overhead.

cs.AI↗

arXiv2026

Decode-Branch Transformers: Decoupling the Primary Prefill Path from Additional Decode Computation

As large language models serve ever more requests, cumulative inference cost is growing relative to the one-time cost of training. In typical serving, prompt prefill runs in parallel and is compute-bound, whereas autoregressive decode is sequential and memory-traffic-bound. Conventional width or depth scaling raises both costs together, since every added layer is evaluated in both phases and enlarges the weights read at each decode step. We instead ask whether additional learned computation can be allocated to continuation prediction while preserving prompt-wide primary computation and a single KV cache. We realize this with the Decode-Branch Transformer. Its primary path alone processes the prompt and writes the KV cache; the decode branch is omitted during prefill and activated only from the final prompt position onward, adding continuation computation without writing state or affecting the primary path. The paths share attention, MLP, and output matrices, using separate token embeddings with lightweight coupling. Grouped decode reuses loaded weight tiles and the primary KV cache across both paths, so the added arithmetic does not proportionally increase dominant memory traffic or decode latency. Across matched-token comparisons, Decode-Branch achieves lower validation loss across architectures and data settings. In MoE models, the primary and branch expert fan-outs become independent knobs for trading prompt cost, decode cost, and predictive quality. We study two expert-allocation regimes, holding prefill or decode computation fixed, and expose a prefill-decode-quality trade-off enabled by phase-specific expert allocation.

cs.AI↗