We present a novel reinforcement learning (RL) environment designed to both optimize industrial sorting systems and study agent behavior in evolving spaces. In simulating material flow within a sorting process our environment follows the idea of a digital twin, with operational parameters like belt speed and occupancy level. To reflect real-world challenges, we integrate common upgrades to industrial setups, like new sensors or advanced machinery. It thus includes two variants: a basic version focusing on discrete belt speed adjustments and an advanced version introducing multiple sorting modes and enhanced material composition observations. We detail the observation spaces, state update mechanisms, and reward functions for both environments. We further evaluate the efficiency of common RL algorithms like Proximal Policy Optimization (PPO), Deep-Q-Networks (DQN), and Advantage Actor Critic (A2C) in comparison to a classical rule-based agent (RBA). This framework not only aids in optimizing industrial processes but also provides a foundation for studying agent behavior and transferability in evolving environments, offering insights into model performance and practical implications for real-world RL applications.

Generating human-like and adaptive trajectories is essential for autonomous driving in dynamic environments. While generative models have shown promise in synthesizing feasible trajectories, they often fail to capture the nuanced variability of human driving styles due to dataset biases and distributional shifts. To address this, we introduce TrajHF, a human feedback-driven finetuning framework for generative trajectory models, designed to align motion planning with diverse driving preferences. TrajHF incorporates multi-conditional denoiser and reinforcement learning with human feedback to refine multi-modal trajectory generation beyond conventional imitation learning. This enables better alignment with human driving preferences while maintaining safety and feasibility constraints. TrajHF achieves PDMS of 93.95 on NavSim benchmark, significantly exceeding other methods. TrajHF sets a new paradigm for personalized and adaptable trajectory generation in autonomous driving.

Popular safe Bayesian optimization (BO) algorithms learn control policies for safety-critical systems in unknown environments. However, most algorithms make a smoothness assumption, which is encoded by a known bounded norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it remains unclear how to reliably obtain the RKHS norm of an unknown function. In this work, we propose a safe BO algorithm capable of estimating the RKHS norm from data. We provide statistical guarantees on the RKHS norm estimation, integrate the estimated RKHS norm into existing confidence intervals and show that we retain theoretical guarantees, and prove safety of the resulting safe BO algorithm. We apply our algorithm to safely optimize reinforcement learning policies on physics simulators and on a real inverted pendulum, demonstrating improved performance, safety, and scalability compared to the state-of-the-art.

In safe reinforcement learning, agent needs to balance between exploration actions and safety constraints. Following this paradigm, domain transfer approaches learn a prior Q-function from the related environments to prevent unsafe actions. However, because of the large number of false positives, some safe actions are never executed, leading to inadequate exploration in sparse-reward environments. In this work, we aim to learn an efficient state representation to balance the exploration and safety-prefer action in a sparse-reward environment. Firstly, the image input is mapped to latent representation by an auto-encoder. A further contrastive learning objective is employed to distinguish safe and unsafe states. In the learning phase, the latent distance is used to construct an additional safety check, which allows the agent to bias the exploration if it visits an unsafe state. To verify the effectiveness of our method, the experiment is carried out in three navigation-based MiniGrid environments. The result highlights that our method can explore the environment better while maintaining a good balance between safety and efficiency.

Many online advertising platforms provide advertisers with auto-bidding services to enhance their advertising performance. However, most existing auto-bidding algorithms fail to accurately capture the auto-bidding problem formulation that the platform truly faces, let alone solve it. Actually, we argue that the platform should try to help optimize each advertiser's performance to the greatest extent -- which makes $\epsilon$-Nash Equilibrium ($\epsilon$-NE) a necessary solution concept -- while maximizing the social welfare of all the advertisers for the platform's long-term value. Based on this, we introduce the \emph{Nash-Equilibrium Constrained Bidding} (NCB), a new formulation of the auto-bidding problem from the platform's perspective. Specifically, it aims to maximize the social welfare of all advertisers under the $\epsilon$-NE constraint. However, the NCB problem presents significant challenges due to its constrained bi-level structure and the typically large number of advertisers involved. To address these challenges, we propose a \emph{Bi-level Policy Gradient} (BPG) framework with theoretical guarantees. Notably, its computational complexity is independent of the number of advertisers, and the associated gradients are straightforward to compute. Extensive simulated and real-world experiments validate the effectiveness of the BPG framework.

AI alignment, the challenge of ensuring AI systems act in accordance with human values, has emerged as a critical problem in the development of systems such as foundation models and recommender systems. Still, the current dominant approach, reinforcement learning with human feedback (RLHF) faces known theoretical limitations in aggregating diverse human preferences. Social choice theory provides a framework to aggregate preferences, but was not developed for the multidimensional applications typical of AI. Leveraging insights from a recently published urn process, this work introduces a preference aggregation strategy that adapts to the user's context and that inherits the good properties of the maximal lottery, a Condorcet-consistent solution concept.

Beyond specific settings, many multi-agent learning algorithms fail to converge to an equilibrium solution, and instead display complex, non-stationary behaviours such as recurrent or chaotic orbits. In fact, recent literature suggests that such complex behaviours are likely to occur when the number of agents increases. In this paper, we study Q-learning dynamics in network polymatrix games where the network structure is drawn from classical random graph models. In particular, we focus on the Erdos-Renyi model, a well-studied model for social networks, and the Stochastic Block model, which generalizes the above by accounting for community structures within the network. In each setting, we establish sufficient conditions under which the agents' joint strategies converge to a unique equilibrium. We investigate how this condition depends on the exploration rates, payoff matrices and, crucially, the sparsity of the network. Finally, we validate our theoretical findings through numerical simulations and demonstrate that convergence can be reliably achieved in many-agent systems, provided network sparsity is controlled.

Language model alignment (or, reinforcement learning) techniques that leverage active exploration -- deliberately encouraging the model to produce diverse, informative responses -- offer the promise of super-human capabilities. However, current understanding of algorithm design primitives for computationally efficient exploration with language models is limited. To better understand how to leverage access to powerful pre-trained generative models to improve the efficiency of exploration, we introduce a new computational framework for RL with language models, in which the learner interacts with the model through a sampling oracle. Focusing on the linear softmax model parameterization, we provide new results that reveal the computational-statistical tradeoffs of efficient exploration: 1. Necessity of coverage: Coverage refers to the extent to which the pre-trained model covers near-optimal responses -- a form of hidden knowledge. We show that coverage, while not necessary for data efficiency, lower bounds the runtime of any algorithm in our framework. 2. Inference-time exploration: We introduce a new algorithm, SpannerSampling, which obtains optimal data efficiency and is computationally efficient whenever the pre-trained model enjoys sufficient coverage, matching our lower bound. SpannerSampling leverages inference-time computation with the pre-trained model to reduce the effective search space for exploration. 3. Insufficiency of training-time interventions: We contrast the result above by showing that training-time interventions that produce proper policies cannot achieve similar guarantees in polynomial time. 4. Computational benefits of multi-turn exploration: Finally, we show that under additional representational assumptions, one can achieve improved runtime (replacing sequence-level coverage with token-level coverage) through multi-turn exploration.

In this note, we examine the aggregation of preferences achieved by the Group Policy Optimisation (GRPO) algorithm, a reinforcement learning method used to train advanced artificial intelligence models such as DeepSeek-R1-Zero and DeepSeekMath. The GRPO algorithm trains a policy using a reward preference model, which is computed by sampling a set of outputs for a given context, observing the corresponding rewards, and applying shift-and-scale normalisation to these reward values. Additionally, it incorporates a penalty function to discourage deviations from a reference policy. We present a framework that enables us to characterise the stationary policies of the GRPO algorithm. This analysis reveals that the aggregation of preferences differs fundamentally from standard logarithmic pooling, which is implemented by other approaches such as RLHF. The precise form of preference aggregation arises from the way the reward preference model is defined and from the penalty function, which we show to essentially correspond to the reverse Kullback-Leibler (KL) divergence between the aggregation policy and the reference policy. Interestingly, we demonstrate that for groups of size two, the reward preference model corresponds to pairwise comparison preferences, similar to those in other alignment methods based on pairwise comparison feedback. We provide explicit characterisations of the aggregate preference for binary questions, for groups of size two, and in the limit of large group size. This provides insights into the dependence of the aggregate preference on parameters such as the regularisation constant and the confidence margin of question answers. Finally, we discuss the aggregation of preferences obtained by modifying the GRPO algorithm to use direct KL divergence as the penalty or to use rewards without scale normalisation.

Predictive models of the future are fundamental for an agent's ability to reason and plan. A common strategy learns a world model and unrolls it step-by-step at inference, where small errors can rapidly compound. Geometric Horizon Models (GHMs) offer a compelling alternative by directly making predictions of future states, avoiding cumulative inference errors. While GHMs can be conveniently learned by a generative analog to temporal difference (TD) learning, existing methods are negatively affected by bootstrapping predictions at train time and struggle to generate high-quality predictions at long horizons. This paper introduces Temporal Difference Flows (TD-Flow), which leverages the structure of a novel Bellman equation on probability paths alongside flow-matching techniques to learn accurate GHMs at over 5x the horizon length of prior methods. Theoretically, we establish a new convergence result and primarily attribute TD-Flow's efficacy to reduced gradient variance during training. We further show that similar arguments can be extended to diffusion-based methods. Empirically, we validate TD-Flow across a diverse set of domains on both generative metrics and downstream tasks including policy evaluation. Moreover, integrating TD-Flow with recent behavior foundation models for planning over pre-trained policies demonstrates substantial performance gains, underscoring its promise for long-horizon decision-making.