LACMAS: Learning to Act and Cooperate

• LACMAS is a trajectory-driven framework enabling agents to adapt local actions and adjust cooperation weights based on historical optimization trajectories.
• It employs a hybrid approach combining a low-level swarm optimization layer with a high-level LLM-guided adaptation to balance exploration and convergence.
• The framework demonstrates versatility by addressing challenges in distributed optimization, communication-constrained MARL, and ad hoc teamwork under partial observability.

Learning to Act and Cooperate (LACMAS), written as LAC-MAS in the named framework introduced for distributed black-box consensus optimization, denotes a trajectory-driven approach in which agents adapt both their internal action behaviors and their external cooperation patterns from historical optimization trajectories (Qin et al., 1 May 2026). A broader reading suggested by adjacent literature is that LACMAS also names a research agenda in which decentralized agents must learn not only what to do locally, but also how, when, and with whom to cooperate under partial observability, partner uncertainty, heterogeneous goals, imperfect communication, and adaptive social response (Weil et al., 2023).

1. Named framework and conceptual scope

In its narrow, explicit sense, LAC-MAS is a framework for distributed black-box consensus optimization on a fixed connected communication graph $G=(V,E)$, where each agent $i\in V$ has a local black-box objective $f_i:\mathbb{R}^D\to\mathbb{R}$, can communicate only with neighbors $N_i$, and must improve the global objective

$f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$

while enforcing consensus. The equivalent constrained form is

$$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$

The defining constraints are that only local function queries are allowed, communication is limited to neighbors in a fixed sparse graph, agents lack global state access, and the setting is often heterogeneous and nonconvex (Qin et al., 1 May 2026).

The phrase “learning to act and cooperate” also aligns with several neighboring lines of work. Those lines formulate the same underlying challenge in different mathematical languages: POSGs under unreliable communication, Dec-POMDPs for ad hoc teamwork with unseen partners, repeated games with adaptive opponents or partners, and heterogeneous-goal teamwork in which cooperation itself becomes a meta-level decision (Charakorn et al., 2021). This suggests that LACMAS is not a single problem class with one canonical formalization, but a family of settings in which action selection and cooperation policy must be learned jointly.

2. Core mechanism of LAC-MAS

The official LAC-MAS framework separates adaptation into learning to act and learning to cooperate. Learning to act concerns local search behavior in each agent’s own black-box space. Learning to cooperate concerns how much weight an agent assigns to each neighbor during decentralized consensus formation. The architecture is deliberately hybrid: a low-level execution layer runs swarm-style optimization continuously, while a high-level guidance layer uses LLMs to reshape internal search coefficients and neighbor-aggregation weights from trajectory summaries rather than from end-to-end control (Qin et al., 1 May 2026).

Each agent $i$ maintains a local particle population $\{x_{i,p}^{(t)}\}_{p=1}^{P}$, with centroid

$$\mu_i^{(t)} = \frac{1}{P}\sum_{p=1}^{P} x_{i,p}^{(t)}$$

and particle divergence

$$D_i^{(t)} = \sum_{p=1}^{P} \left\|x_{i,p}^{(t)}-\mu_i^{(t)}\right\|^2.$$

Divergence functions as a regime indicator: large $i\in V$0 corresponds to exploration, while small $i\in V$1 corresponds to convergence or local exploitation. Each agent carries a discrete internal coefficient set

$i\in V$2

and selects the active coefficient according to thresholds $i\in V$3: $i\in V$4 The subsequent update is

$i\in V$5

where $i\in V$6 is the stochastic modulation vector from the swarm backbone. The intended effect is to improve the balance between exploration, convergence, and local escape without abandoning decentralization (Qin et al., 1 May 2026).

Cooperation is likewise made adaptive. For each neighbor $i\in V$7, the framework summarizes trajectory information by

$i\in V$8

encoding recent objective quality, particle divergence, and state variation. The LLM receives only local and neighbor trajectory summaries and outputs candidate cooperation weights over $i\in V$9. After normalization and projection to ensure nonnegativity, graph compatibility, and unit sum, agent $f_i:\mathbb{R}^D\to\mathbb{R}$0 performs the external update

$f_i:\mathbb{R}^D\to\mathbb{R}$1

Cooperation therefore becomes trajectory-aware and utility-sensitive rather than a fixed uniform average over neighbors (Qin et al., 1 May 2026).

3. Trajectory guidance, scheduling, and consensus guarantees

A distinctive feature of LAC-MAS is that the LLM is not the optimizer itself. It is a sparse high-level guidance module invoked only at scheduled times. Internal-action adaptation is useful when local search regimes shift, whereas cooperation adaptation is refreshed more regularly as neighbor usefulness changes. To regulate this, the framework introduces Phased Cognitive Guidance (PCG) based on a calibrated horizon $f_i:\mathbb{R}^D\to\mathbb{R}$2. The cooperation-refresh gate is

$f_i:\mathbb{R}^D\to\mathbb{R}$3

while the internal-action refresh gate is

$f_i:\mathbb{R}^D\to\mathbb{R}$4

After the horizon $f_i:\mathbb{R}^D\to\mathbb{R}$5, internal guidance is deactivated: $f_i:\mathbb{R}^D\to\mathbb{R}$6 The paper interprets this as a four-stage progression: trajectory accumulation, learning to act, learning to act and cooperate, and consensus-oriented cooperation (Qin et al., 1 May 2026).

This schedule is resource-aware in two senses. First, it reduces expensive LLM calls. Second, it matches the form of adaptation to the optimization phase: early trajectory collection, mid-course internal adaptation, combined adaptation, and finally consensus-biased coordination. Algorithmically, the loop computes centroid and divergence, summarizes local and neighbor trajectories, conditionally queries the LLM, selects the divergence-triggered internal coefficient, updates particles, normalizes cooperation weights, performs the weighted consensus update, and appends to history (Qin et al., 1 May 2026).

The framework also supplies a consensus analysis. Under a fixed connected graph, normalized cooperation weights, bounded internal coefficients and perturbations, a consensus-capable swarm backbone, and asymptotically vanishing late-stage perturbations, the closed-loop dynamics are written as

$f_i:\mathbb{R}^D\to\mathbb{R}$7

Theorem 4.1 states

$f_i:\mathbb{R}^D\to\mathbb{R}$8

Within the paper’s assumptions, adaptation of acting and cooperating is therefore designed not to destroy the consensus structure it seeks to improve (Qin et al., 1 May 2026).

4. Adjacent multi-agent paradigms

A major adjacent paradigm studies cooperation through explicit communication rather than through consensus weighting. In a cooperative POSG with private observations, decentralized execution, and a limited unreliable channel, agents select both an environment action and a message size $f_i:\mathbb{R}^D\to\mathbb{R}$9, with message-size selection learned by independent DQNs and message content produced by size-specific encoders. In the proposed pipeline, agents observe, receive prior messages, encode local information, choose action, choose message size, generate a message, transmit through a slotted stochastic limited-capacity channel, and then use surviving messages at the next step. In POMNIST, a two-step cooperative digit-prediction benchmark, adaptive communication improves over non-adaptive baselines; continuous communication performs best, pseudo-gradient discrete communication is next, and DRU performs worst among the tested message types. In traffic junction, communication still improves success over no communication, but adaptive message-size selection is less stable and sometimes worse than fixed-size communication (Weil et al., 2023).

A second paradigm concerns ad hoc teamwork with unseen partners. One meta-RL formulation treats the partner distribution as the meta-distribution and trains recurrent policies whose hidden state acts as the fast adaptation mechanism. In a Dec-POMDP with shared reward, the recurrent models receiving reward input, especially r-RNN and ar-RNN, perform best on unseen partners. Reported average test performance for ar-RNN is around 35.03 in the Lever Coordination Game and 34.94 in the Discrete Speaker-Listener Game. The same work reports robustness to much longer horizons (500 steps vs. 50) and to partner switching within an episode, and also strong ad hoc performance against independently learned partners, about 32.62 in LC and 25.63 in DSL (Charakorn et al., 2021).

A third paradigm addresses completely unknown teammates rather than merely unseen teammates. The method OTLPP combines PLASTIC-Policy with transfer learning via parameter sharing. After identifying the most similar prior teammate model, it initializes a fresh DQN for the current teammate from the selected source DQN rather than learning from scratch. In Half Field Offense, a $N_i$0 vs. $N_i$1 setting with five independently developed teammates—agent2d, aut, gliders, helios, and receptivity—the reported 100,000-episode scores are: agent2d 0.37 vs. 0.40, helios 0.61 vs. 0.62, aut 0.55 vs. 0.58, gliders 0.53 vs. 0.51, and receptivity 0.47 vs. 0.52 for PLASTIC-Policy and OTLPP respectively (Neves et al., 2022).

A fourth paradigm generalizes ad hoc teamwork to heterogeneous goals. In that setting, an agent must decide whether a goal should be pursued jointly, alone, or not at all, because teammate goals may only partially overlap. The method GRILL separates high-level goal selection by PPO from low-level goal-conditioned control learned by offline imitation, while GRILL-M augments this with an auxiliary teammate-modeling module. Across extended Cooperative Reaching and Level-Based Foraging, GRILL and GRILL-M outperform PPO, LIAM, and OMG. The effect of teammate modeling is explicitly tied to goal observability: at $N_i$2, GRILL-M is 5.5% better; at $N_i$3, 95.2% better; and with the cue $N_i$4 removed entirely, 142.6% better (Taylor-Davies et al., 7 Mar 2026).

5. Incentives, social structure, and theoretical boundaries

Not all act-and-cooperate systems begin from a fixed reward. One strand evolves the reward signal itself. In Pong, reward mutation is restricted to three predefined screen regions $N_i$5, each taking value $N_i$6 or $N_i$7, yielding $N_i$8 possible reward signals. Optimizing the goals of winning, losing, and cooperation leads to final surviving reward signals 100, 000, and 110, respectively. The paper reports that evolved rewards can be more stable than score-based baselines, with 110 especially notable as a non-obvious but strong cooperative signal (Muszynski et al., 2021).

Another strand models cooperation through reputation. In the Clean Up social dilemma, five agents interact in a $N_i$9 world containing an orchard and a polluted river; agents collect apples for individual reward, clean pollution with a water-beam tool, and can punish others with a ticketing tool. Cooperation depends on where and when agents clean, not just how much they contribute. The model uses independent multi-agent A2C with heterogeneous intrinsic reputational terms, with $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$0, $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$1, temporal smoothing $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$2 with $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$3, and anonymous visibility limited by $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$4 under the $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$5 norm. Under identifiability, both humans and agents contribute more, obtain higher collective return, exhibit less territoriality, and show more turn-taking than under anonymity (McKee et al., 2021).

A central theoretical boundary is that learning to cooperate with adaptive partners is not generically solvable. In infinitely repeated matrix games, adaptive regret compares the learner’s long-run payoff with that of the best expert strategy against the partner’s actual adaptive response. The paper proves that for any learning algorithm, there exists an open-ended adaptive partner strategy that induces nontrivial adaptive regret, even in an $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$6 coordination game with fixed-action experts. The underlying dilemma is structural: a learner that eventually commits can be exploited after commitment, whereas a learner that keeps exploring can be denied sufficiently long evaluation windows for any expert (Loftin et al., 2022).

A related population-level result studies finitely repeated two-player general-sum matrix games with private utilities. There, a target population is assumed to be consistent in the sense of bounded external regret and compatible in the sense that pairwise interaction reaches at least some Pareto-optimal Nash equilibrium with high probability. Those assumptions are shown to be insufficient for zero-shot cooperation by an outsider. Offline observations are therefore introduced, yielding a dataset $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$7, lower bounds showing that naive imitation can require sample complexity $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$8, and an imitate-then-commit upper bound whose dependence is on a coordination prefix $f(x)=\frac{1}{N}\sum_{i=1}^{N} f_i(x)$9 rather than the full horizon $$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$0 (Loftin et al., 2024).

6. Empirical domains, interpretations, and unresolved questions

Across the literature, LACMAS-related work is tested in markedly different domains.

Setting	Representative environments	Primary cooperation issue
Distributed optimization	$$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$1–$$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$2, wireless sensor network localization	Consensus, trajectory-aware neighbor weighting (Qin et al., 1 May 2026)
Communication-constrained MARL	POMNIST, traffic junction	Message content and message-size adaptation under drops and collisions (Weil et al., 2023)
Ad hoc teamwork	Lever Coordination, DSL, HFO, Cooperative Reaching, LBF	Unseen teammates, unknown teammates, heterogeneous goals (Charakorn et al., 2021)

Within distributed optimization proper, LAC-MAS is evaluated on 10 distributed black-box benchmark functions $$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$3–$$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$4 with 100 decision variables and 20 agents, against MASOIE, GFPDO, RGF, and DA-PSO, using final fitness, cumulative communication cost until convergence, and disagreement over iterations. Convergence is declared when disagreement drops below $$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$5. The paper also reports a transfer study on wireless sensor network multi-target localization, in which LAC-MAS attains the lowest estimation error across different numbers of targets (Qin et al., 1 May 2026).

Several misconceptions are corrected by the broader record. LACMAS is not reducible to a single communication protocol, a single MARL architecture, or a single assumption of shared reward. Some work assumes full cooperation and shared returns; some assumes heterogeneous private goals; some assumes explicit communication; some addresses cooperation without prior coordination; and some proves that unrestricted adaptive cooperation is impossible. Cooperation is also not uniformly desirable: one paper makes the decision of when to cooperate the central problem, rather than assuming that teamwork is always beneficial (Taylor-Davies et al., 7 Mar 2026).

The limitations are similarly heterogeneous. In LAC-MAS itself, the communication graph is fixed and connected, cooperation only reweights existing neighbors, the schedule depends on a calibrated horizon $$\min \frac{1}{N}\sum_{i=1}^{N} f_i(x_i)\quad \text{s.t. } x_i=x_j,\ \forall i,j.$$6, and the theoretical guarantee relies on boundedness and vanishing-perturbation assumptions (Qin et al., 1 May 2026). In adaptive communication over imperfect channels, the message-size value target can have high variance, performance degrades when reliability is poor and coordination demand is high, and the channel model remains simplistic (Weil et al., 2023). In heterogeneous-goal teamwork, the experiments are limited to fully observable environments, two agents, and an offline-first low-level policy (Taylor-Davies et al., 7 Mar 2026). In unknown-teammate transfer, performance still depends on identifying a meaningful source policy (Neves et al., 2022). In meta-RL ad hoc teamwork, generalization improves with both the quantity and diversity of training partners, implying that narrow partner distributions sharply limit robustness (Charakorn et al., 2021).

Taken together, the literature supports a precise interpretation. In the narrow sense, LAC-MAS is a trajectory-driven framework that couples adaptive local search with adaptive decentralized cooperation in distributed black-box consensus optimization (Qin et al., 1 May 2026). In the broader sense suggested by adjacent work, LACMAS denotes a research program on how agents learn action, communication, coordination, adaptation, and social response jointly—under exactly those conditions where cooperation is useful, difficult, and often only partially identifiable from interaction alone.