arXiv subjects

Jakob Foerster

Publications and source records attributed to Jakob Foerster.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Offline Multi-Agent Reinforcement Learning with Latent World Models

Model-based offline multi-agent reinforcement learning (MARL) provides a promising approach to multi-agent decision-making under partial observability, where the global state is unavailable from offline data. However, limited dataset coverage can lead to substantial out-of-distribution (OOD) model errors, which may mislead policy optimization and degrade downstream performance. Existing model-based offline MARL methods typically rely on access to global states or mitigate model errors through pessimistic or conservative policy optimization, leaving the reliability and refinement of learned world models less explored. We propose a Bayesian offline MARL framework that infers latent global states from decentralized observation-action histories and iteratively refines a posterior world model using only offline data. Building on posterior information loss, we extend this criterion to the multi-agent setting as multi-agent posterior information loss (MPIL), which provides a reliability measure for world model refinement and offline evaluation. Theoretically, we establish an upper bound on policy regret that is monotonic in MPIL and further characterize its dependence on the size and state-joint-action coverage of the offline dataset. Experiments on partially observable multi-agent variants of D4RL MuJoCo tasks demonstrate competitive policy performance across diverse offline data conditions, while MPIL-guided refinement improves world model prediction and downstream policy performance. These results support a principled connection between world model reliability, offline data coverage, and policy performance in partially observable offline MARL.

cs.MA↗

arXiv2026

Understanding the Inner Workings of a State-Space Foundation Model for Limit Order Books

Autoregressive foundation models offer state-of-the-art capabilities to simulate the market by generating the message flow of limit order books (LOBs). Yet, without understanding their inner workings, research directions are hard to narrow and practical use in real-world trading environments remains uncertain. This study therefore asks what these models actually learn about market microstructure. We find that, similarly to games where sequence models build an internal representation of the board, an 8.2M-parameter Mamba-3 state-space model trained autoregressively on the tokenized message stream of eight large-cap US equities learns an internal representation of the market and its dynamics. In particular, order-flow imbalance, a central driver of short-horizon price moves, is decodable at $R^2 \approx 0.59$, far above controls and baselines. This representation extends to unseen stocks, suggesting that these models learn general representations rather than ticker-specific patterns. The model also generalizes across metrics beyond order-flow imbalance: results hold across traded volume and volatility. Additionally, the representation is causally steerable: pushing the state along a feature's axis shifts the model's next-message beliefs as that feature implies, monotonically in dose, consistent with the emergence of a world model.

q-fin.TR↗

arXiv2026

Adversarial Post-Training of Foundation Models for High-Frequency Trading

While autoregressive foundation models trained on limit order book (LOB) data show state-of-the-art performance for market simulation, pre-training with cross-entropy neither penalizes the compounding of sampling errors over free-running rollouts nor targets desired market properties. We introduce a post-training method for LOB foundation models using a Wasserstein generative adversarial network (GAN) objective. A critic, trained online on rollouts through the true, non-differentiable matching engine, guides updates from evolution strategies over rank-4 LoRA perturbations of the pre-trained generator, under a KL trust region. For efficiency, we use EGGROLL (Evolution Guided GeneRal Optimisation via Low-rank Learning), a memory-efficient variant of evolution strategies. On a held-out panel, adversarial post-training improves LOB-Bench realism by 17.6% (WS-21) and 17.0% (Mean-$L_1$), while selection-matched random-perturbation and compute-matched continued-pre-training controls yield no improvement. Post-training is thus a necessary stage that more pre-training does not replace. Per-position divergence measurements show that it slows error accumulation over 500-message rollouts from $3.1\times$ to $2.3\times$. Adversarial post-training is also inexpensive, requiring under 50M training tokens and 12 GPU-hours per seed, three orders of magnitude below the 48B-token pre-training budget. Ablations over critic inputs, optimizers, and the population-rollout trade-off, together with an analysis of reward hacking, yield practical design guidelines for adversarial post-training.

cs.LG↗

arXiv2026

LOB-Impact Benchmark: Emergent Market Impact in Generative Limit Order Book Models

Realistic market impact is essential for generative limit order book (LOB) models to serve as world models for trading agents. If a simulator misprices this mechanism, agents learn policies that are optimal in the simulator but wrong in the real market. Existing metrics assess generated streams purely through distributional comparison with historical data, leaving counterfactual response to an agent's own orders largely unexplored. Here, we show that market impact emerges naturally in neural LOB generators trained solely for next-token prediction. We inject execution-style metaorders into the generated message flow of five autoregressive models across five NASDAQ stocks and measure the response using estimators from the empirical impact literature, validated on baselines whose physics is known in advance. Our benchmark evaluates any message-level generator in three phases: free generation (reading order-flow persistence against price diffusivity); metaorder injection (yielding the impact law's exponent and amplitude); and a post-execution window (measuring relaxation). In addition, comparing each visible injection to a blind, simulator-only control isolates the model's learned response from standard book mechanics. For every model on every stock, we measure how the impact responds as a function of cumulative metaorder participation. Interestingly, we observe emergent impact in generative models of market data, with exponents in the range of 0.63 to 1.21, slightly above the traditional 0.5 of the square-root law of impact. In the family of models tested, we are so far unable to observe impact decay during relaxation. We tentatively attribute this to the still-short context windows of the models. We release the benchmark as open source to validate future generative models for market data.

q-fin.TR↗

arXiv2026

Q-Shaped Options for Hierarchical Reinforcement Learning

Learning to tackle long-horizon, goal-conditioned tasks requires an agent to reason over extended timescales and act across a broad range of states. In principle, Hierarchical Reinforcement Learning (HRL) addresses both challenges through the interaction between action (temporal) and state (spatial) abstraction. First, using an action abstraction to represent temporally extended behaviour as options reduces the effective decision horizon. Second, enabling different state abstractions at each level of the decision process permits greater data aggregation for learning. However, realising these two benefits of a hierarchical policy depends on learning an appropriate action abstraction. Current HRL algorithms fail in one of two ways. Some discard distinctions between options needed for optimal control, undermining hierarchy altogether. Others retain unnecessary distinctions, preserving horizon reduction, but forfeiting coarser state abstraction. In this work, we characterise three desiderata for an action abstraction. We introduce Q-Shaped Options (QSO) to address all three. QSO builds on an architecture with distinct state-value functions, Q functions and policies at each level of the hierarchy. It learns the action abstraction between consecutive levels as a shared encoder shaped by their respective Q functions. The low-level Q function uses the option as a goal, encouraging the abstraction to retain distinctions necessary for optimal control. The high-level Q function uses it as an action, encouraging unnecessary distinctions to be discarded. Across offline goal-conditioned locomotion and manipulation environments, QSO learns semantically meaningful option spaces and outperforms baselines, achieving non-zero performance in tasks where all other evaluated algorithms fail.

cs.AI↗

arXiv2026

GitSwarm: Decentralized Compounding Inference

Long-horizon problem solving and scientific research require computation to accumulate across successive attempts. Partial solutions, experimental findings, and unsuccessful approaches can inform later work, yet most inference-time computation is organized around individual trajectories or candidates rather than a persistent body of reusable work. We call this paradigm compounding inference: organizing inference-time computation so that intermediate work persists and can be inspected, extended, combined, or challenged by subsequent computation. We instantiate compounding inference in GitSwarm, an asynchronous system where homogeneous agents independently decide how to advance a task while collaborating through structured persistent memory. Agents explore, experiment, verify, refine, and synthesize previous work in a shared, branch-able Git repository. Atomic commits preserve intermediate artifacts, while explicit semantic dependencies record how later contributions build on work across branches. We evaluate GitSwarm on long-horizon problem solving and sustained GPU-backed experimental research. On IMOProofBench-Advanced, GitSwarm solves all 30 problems in one run using GPT-5.5. On ProgramBench, it achieves a $79.4\%$ mean score, versus $65.1\%$ for the strongest reported baseline under the stated budget. On three neural architecture research tasks (Residual Matrix Transformer, Looped Transformer, NanoChat), GitSwarm improves upon the starting architectures through successive experimentation. Beyond final performance, we measure whether computation accumulates: on ProgramBench, $94.7\%$ of contributions are subsequently built upon, while the selected solution's ancestry covers $82-93\%$ of the contribution graph. These results show that inference-time computation can accumulate across otherwise independent episodes, forming an evolving body of work that subsequent inference can reuse.

cs.AI↗

arXiv2026

Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of 113 predominantly unsolved problems spanning eight domains in mathematics and the mathematical sciences, paired with an open-source evaluation framework for automated verification. Our benchmark targets the generator-verifier gap: problems where discovery is hard and requires meaningful mathematical insight, but verification is computationally straightforward. This contrasts with most existing research-level benchmarks, which instead rely on formal proof verification or manual review, both of which are expensive to scale. Because these solutions are unknown, HorizonMath is resistant to data contamination, and most state-of-the-art models score under 10%. Using this framework, we identify six novel solutions to research problems that either resolve previously open questions or improve on the best-known published results, with GPT-5.4 Pro and GPT-5.6 Sol each discovering three of these solutions. Across seven frontier model families, reasoning efficiency and behavior also vary substantially. We release HorizonMath as an open challenge and a growing community resource, where each verified solution is a candidate contribution to the mathematical literature.

cs.LG↗

arXiv2026

Recurrent Reinforcement Learning with Memoroids

Memory models such as Recurrent Neural Networks (RNNs) and Transformers address Partially Observable Markov Decision Processes (POMDPs) by mapping trajectories to latent Markov states. Neither model scales particularly well to long sequences, especially compared to an emerging class of memory models called Linear Recurrent Models. We discover that the recurrent update of these models resembles a monoid, leading us to reformulate existing models using a novel monoid-based framework that we call memoroids. We revisit the traditional approach to batching in recurrent reinforcement learning, highlighting theoretical and empirical deficiencies. We leverage memoroids to propose a batching method that improves sample efficiency, increases the return, and simplifies the implementation of recurrent loss functions in reinforcement learning.

cs.LG↗

arXiv2026

The Yokai Learning Environment: Tracking Beliefs Over Space and Time

The ability to cooperate with unknown partners is a central challenge in cooperative AI and widely studied in the form of zero-shot coordination (ZSC), which evaluates an algorithm by measuring the performance of independently trained agents when paired. The Hanabi Learning Environment (HLE) has become the dominant benchmark for ZSC, but recent work has achieved near-perfect inter-seed cross-play performance, limiting its ability to track algorithmic progress. We introduce the Yokai Learning Environment (YLE) - an open-source multi-agent RL benchmark in which effective collaboration requires building common ground by tracking and updating beliefs over moving cards, reasoning under ambiguous hints, and deciding when to terminate the game based on inferred shared knowledge - features absent in the HLE, where beliefs are tied to hand slots and hints are truthful by rule. We evaluate the leading ZSC methods, including High-Entropy IPPO, Other-Play, and Off-Belief Learning, which achieve near-perfect inter-seed cross-play in the HLE, and show that in the YLE they exhibit persistent SP-XP gaps, degraded early-ending calibration, and weaker belief representations in cross-play, indicating failure to maintain consistent internal models with unseen partners. Methods that perform best in the HLE do not perform best in the YLE, indicating that progress measured on a single benchmark may not generalise. Together, these results establish YLE as a challenging new ZSC benchmark.

cs.AI↗

arXiv2026

Is Inter-Seed Cross-Play Enough? Evaluating the Robustness of Zero-Shot Coordination Algorithms to Implementation Details

AI agents deployed in real-world settings must be capable of coordinating with humans and other AI agents they have not encountered before. Zero-shot coordination (ZSC) algorithms aim to achieve this by specifying high-level learning rules such that independently engineered agents can coordinate with each other at test time. Rigorous evaluation of ZSC algorithms remains difficult: ideally, multiple independent implementations of each proposed algorithm must be used, reflecting the variation that arises when independent parties interpret and implement the same specification. In practice, however, ZSC algorithms have almost exclusively been evaluated using a single implementation trained across different random seeds, with only a handful of works additionally varying the neural network architecture. This leaves open questions about robustness to specification ambiguities and implementation details. In this work, we provide the first systematic evaluation of this robustness. We introduce a new evaluation scheme, cross-implementation cross-play, varying implementation details that prior work has shown to affect the performance of multi-agent reinforcement learning (MARL) algorithms, and we evaluate Other-Play, a popular ZSC algorithm, with this scheme. Our findings are encouraging and suggest that, for Other-Play, the standard ZSC evaluation is, in fact, a reasonable proxy for this more thorough cross-implementation evaluation.

cs.AI↗

arXiv2026

Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments

An agent's performance stagnating at a suboptimal level is a common problem in deep on-policy RL. Focusing on PPO, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimisation challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. Looking deeper, PPO alternates between sampling rollouts from several parallel environments online using the current policy (which we call the "outer loop") and performing repeated minibatch SGD steps against this offline dataset (the "inner loop"). In our work, we abstract away the inner loop, and conceptually model the outer loop as standard stochastic optimisation. The step size is then controlled by the regularisation strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This framing predicts that, much like in SGD, if the outer step size is too large relative to the noise, updates become uninformative and lead to the policy thrashing around a local optimum instead of converging. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We validate the predictions of our model and conclude that increasing the number of parallel environments is a simple way to avoid these plateaus by simultaneously altering both these factors. Applying our analysis and scaling PPO to more than 1M parallel environments enables monotonic performance improvement up to one trillion transitions and leads to vastly superior performance compared to prior baselines in a complex open-ended domain.

cs.LG↗

arXiv2026

Autodata: An agentic data scientist to create high quality synthetic data

We introduce Autodata, a general method that enables AI agents to act as data scientists who build high quality training and evaluation data. We show how to train (meta-optimize) such a data scientist agent, so that it learns to create even stronger data. We describe the overall formulation, and a specific practical implementation, Agentic Self-Instruct. We conduct experiments on computer science research tasks, legal reasoning tasks and reasoning with mathematical objects, where we obtain improved results compared to classical synthetic dataset creation methods. Further, meta-optimizing the data scientist agent itself delivers an even larger performance uplift. Agentic data creation provides a way to convert increased inference compute into higher quality model training. Overall, we believe this direction has the potential to change the way we build AI data.

cs.AI↗

arXiv2026

Evolving Many Worlds: Towards Open-Ended Discovery in Petri Dish NCA via Population-Based Training

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".

cs.NE↗

arXiv2026

Modelling Opinion Dynamics at Scale with Deep MARL

Modelling opinion dynamics typically relies on hand-crafted local interaction rules to study emergent macroscopic phenomena such as consensus and polarisation. In contrast, multi-agent reinforcement learning (MARL) enables agents to learn such behaviours directly by optimising simple rewards. To explore the potential of MARL for opinion dynamics, we introduce a GPU-accelerated consensus and truth-finding game that scales to populations of up to 1000 agents, comparable to many real-world social sub-networks. To prevent unrealistic conventions, we extend other-play to general-sum social interactions. We next validate our model on a subset of the Bluesky network by recovering agent importance structures from graph topology alone via a learned attention layer, finding that highly conforming populations most closely match human data. In large social media networks such high levels of conformity significantly reduce collective accuracy and promote dishonest agents that lie to fit in. By contrast, small, dynamic hunter-gatherer networks are less affected; here, conformity can even improve collective agreement. This suggests a mismatch between evolved human conformity heuristics and modern social media environments as a potential contributor to misinformation.

cs.MA↗

arXiv2026

High entropy leads to symmetry-equivariant policies in Dec-POMDPs

We prove that in any Dec-POMDP, sufficiently high entropy regularization ensures that the policy gradient flow with tabular softmax parametrization always converges, for any initialization, to the same joint policy, and that this joint policy is equivariant w.r.t. all symmetries of the Dec-POMDP. In particular, policies coming from different initializations will be fully compatible, in that their cross-play returns are equal to their self-play returns. Through extensive evaluation of independent PPO, arguably the standard baseline deep multi-agent policy gradient algorithm, in the Hanabi, Overcooked and Yokai environments, we find that the entropy coefficient has a massive influence on the cross-play returns between independently trained policies, and that the decrease in self-play returns coming from increased entropy regularization can often be counteracted by greedifying the learned policies after training. In Hanabi in particular we achieve a new SOTA in inter-seed cross-play this way. While we give examples of Dec-POMDPs in which one cannot learn the optimal symmetry-equivariant policy this way, both our theoretical and empirical results suggest that one should consider far higher entropy coefficients during hyperparameter sweeps in Dec-POMDPs than is typically done. Code for our experiments can be found at https://github.com/jforkel/JAX-OBL

cs.LG↗

arXiv2026

Evaluating AI-based Scientific Knowledge Synthesis with Epidemiological Systematic Reviews

Systematic literature reviews (SLRs) are a demanding and high-stakes form of scientific knowledge synthesis that remains underspecified as an evaluation setting for large language models (LLMs). We introduce AgentSLR, a large-scale evaluation harness comprising an SLR automation workflow and an expert annotated dataset covering 16,248 articles, designed to test LLM capabilities across the stages of SLRs in epidemiology. Reference annotations were derived from peer-reviewed studies on WHO priority pathogens and produced by domain experts. The harness evaluates each review stage as a separate unit with dedicated metrics enabling targeted failure analysis. We evaluated five frontier reasoning models and found that no single model dominated across all tasks, showing sub-task specialisation often hidden by aggregate benchmarks. Structured data extraction is a major bottleneck, with no model exceeding an average field-level F1 of 0.67. Estimated costs vary substantially, by up to 96 times across evaluated models. Documented failure modes suggest that the evaluated models are not yet reliable enough for unsupervised deployment in epidemiology, where findings can inform public policy.

cs.IR↗

arXiv2026

Expected Return Symmetries

Symmetry is an important inductive bias that can improve model robustness and generalization across many deep learning domains. In multi-agent settings, a priori known symmetries have been shown to address a fundamental coordination failure mode known as mutually incompatible symmetry breaking; e.g. in a game where two independent agents can choose to move "left'' or "right'', and where a reward of +1 or -1 is received when the agents choose the same action or different actions, respectively. However, the efficient and automatic discovery of environment symmetries, in particular for decentralized partially observable Markov decision processes, remains an open problem. Furthermore, environmental symmetry breaking constitutes only one type of coordination failure, which motivates the search for a more accessible and broader symmetry class. In this paper, we introduce such a broader group of previously unexplored symmetries, which we call expected return symmetries, which contains environment symmetries as a subgroup. We show that agents trained to be compatible under the group of expected return symmetries achieve better zero-shot coordination results than those using environment symmetries. As an additional benefit, our method makes minimal a priori assumptions about the structure of their environment and does not require access to ground truth symmetries.

cs.MA↗

arXiv2026

Recurrent Structural Policy Gradient for Partially Observable Mean Field Games

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) reduce variance while maintaining tractability by leveraging low-dimensional individual state and action spaces and known transition dynamics to compute the exact expected return conditioned on Monte Carlo rollouts of common noise. However, HSMs have not been extended to partially observable settings. We propose Recurrent Structural Policy Gradient (RSPG), the first history-aware HSM for MFGs with public partial information. RSPG achieves an order-of-magnitude faster convergence than model-free RL methods while learning history-aware behaviour, unlike current HSMs. To facilitate research into MFGs, we also introduce MFAX, our JAX-based framework for MFGs that supports both analytic and sample-based mean-field updates. MFAX and usage examples can be found at https://clarisse-wibault.github.io/rspg/.

cs.AI↗