We study multi-agent reinforcement learning (MARL) in infinite-horizon discounted zero-sum Markov games.

Reinforcement learning (RL) has emerged as a pivotal technique for fine-tuning large language models (LLMs) on specific tasks. However, prevailing RL fine-tuning methods predominantly rely on PPO and its variants. Though these algorithms are effective in general RL settings, they often exhibit suboptimal performance and vulnerability to distribution collapse when applied to the fine-tuning of LLMs.

To help address these issues, a natural approach is to consider games with special structures. In this paper, we focus on congestion games.

However, such "black-box" policies lack interpretability and reliability, and often,

Transformers have demonstrated exceptional in-context learning (ICL) capabilities, enabling applications across natural language processing, computer vision, and sequential decision-making. In reinforcement learning, ICL reframes learning as a supervised problem, facilitating task adaptation without parameter updates. Building on prior work leveraging transformers for sequential decision-making, we propose Heuristic Transformer (HT), an in-context reinforcement learning (ICRL) approach that augments the in-context dataset with a belief distribution over rewards to achieve better decision-making. Using a variational auto-encoder (VAE), a low-dimensional stochastic variable is learned to represent the posterior distribution over rewards, which is incorporated alongside an in-context dataset and query states as prompt to the transformer policy. We assess the performance of HT across the Darkroom, Miniworld, and MuJoCo environments, showing that it consistently surpasses comparable baselines in terms of both effectiveness and generalization. Our method presents a promising direction to bridge the gap between belief-based augmentations and transformer-based decision-making.

Pre-trained vision-language-action (VLA) models offer a promising foundation for generalist robot policies, but often produce brittle behaviors or unsafe failures when deployed zero-shot in out-of-distribution scenarios. We present Vision-Language-Action Planning & Search (VLAPS) -- a novel framework and accompanying algorithms that embed model-based search into the inference procedure of pre-trained VLA policies to improve their performance on robotic tasks. Specifically, our method biases a modified Monte Carlo Tree Search (MCTS) algorithm -- run using a model of the target environment -- using action priors defined by the VLA policy. By using VLA-derived abstractions and priors in model-based search, VLAPS efficiently explores language-conditioned robotics tasks whose search spaces would otherwise be intractably large. Conversely, by integrating model-based search with the VLA policy's inference procedure, VLAPS yields behaviors that are more performant than those obtained by directly following the VLA policy's action predictions. VLAPS offers a principled framework to: i) control test-time compute in VLA models, ii) leverage a priori knowledge of the robotic environment, and iii) integrate established planning and reinforcement learning techniques into the VLA inference process. Across all experiments, VLAPS significantly outperforms VLA-only baselines on language-specified tasks that would otherwise be intractable for uninformed search algorithms, increasing success rates by as much as 67 percentage points.

Graphical User Interface (GUI) grounding, the task of mapping natural language instructions to precise screen coordinates, is fundamental to autonomous GUI agents. While existing methods achieve strong performance through extensive supervised training or reinforcement learning with labeled rewards, they remain constrained by the cost and availability of pixel-level annotations. We observe that when models generate multiple predictions for the same GUI element, the spatial overlap patterns reveal implicit confidence signals that can guide more accurate localization. Leveraging this insight, we propose GUI-RC (Region Consistency), a test-time scaling method that constructs spatial voting grids from multiple sampled predictions to identify consensus regions where models show highest agreement. Without any training, GUI-RC improves accuracy by 2-3% across various architectures on ScreenSpot benchmarks. We further introduce GUI-RCPO (Region Consistency Policy Optimization), transforming these consistency patterns into rewards for test-time reinforcement learning. By computing how well each prediction aligns with the collective consensus, GUI-RCPO enables models to iteratively refine their outputs on unlabeled data during inference. Extensive experiments demonstrate the generality of our approach: using only 1,272 unlabeled data, GUI-RCPO achieves 3-6% accuracy improvements across various architectures on ScreenSpot benchmarks. Our approach reveals the untapped potential of test-time scaling and test-time reinforcement learning for GUI grounding, offering a promising path toward more data-efficient GUI agents.