Robots operating in complex and unknown environments frequently require geometric-semantic representations of the environment to safely perform their tasks. While inferring the environment, they must account for many possible scenarios when planning future actions. Since objects' class types are discrete and the robot's self-pose and the objects' poses are continuous, the environment can be represented by a hybrid discrete-continuous belief which is updated according to models and incoming data. Prior probabilities and observation models representing the environment can be learned from data using deep learning algorithms. Such models often couple environmental semantic and geometric properties. As a result, semantic variables are interconnected, causing semantic state space dimensionality to increase exponentially. In this paper, we consider planning under uncertainty using partially observable Markov decision processes (POMDPs) with hybrid semantic-geometric beliefs. The models and priors consider the coupling between semantic and geometric variables. Within POMDP, we introduce the concept of semantically aware safety. Obtaining representative samples of the theoretical hybrid belief, required for estimating the value function, is very challenging. As a key contribution, we develop a novel form of the hybrid belief and leverage it to sample representative samples. We show that under certain conditions, the value function and probability of safety can be calculated efficiently with an explicit expectation over all possible semantic mappings. Our simulations show that our estimates of the objective function and probability of safety achieve similar levels of accuracy compared to estimators that run exhaustively on the entire semantic state-space using samples from the theoretical hybrid belief. Nevertheless, the complexity of our estimators is polynomial rather than exponential.

Partially Observable Markov Decision Processes (POMDPs) provide a robust framework for decision-making under uncertainty in applications such as autonomous driving and robotic exploration. Their extension, $\rho$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $\rho$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $\rho$POMCPOW, an anytime solver that dynamically refines belief representations, with formal guarantees of improvement over time. To mitigate the high computational cost of updating belief-dependent rewards, we propose a novel incremental computation approach. We demonstrate its effectiveness for common entropy estimators, reducing computational cost by orders of magnitude. Experimental results show that $\rho$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

We introduce OmniRL, a highly generalizable in-context reinforcement learning (ICRL) model that is meta-trained on hundreds of thousands of diverse tasks. These tasks are procedurally generated by randomizing state transitions and rewards within Markov Decision Processes. To facilitate this extensive meta-training, we propose two key innovations: 1. An efficient data synthesis pipeline for ICRL, which leverages the interaction histories of diverse behavior policies; and 2. A novel modeling framework that integrates both imitation learning and reinforcement learning (RL) within the context, by incorporating prior knowledge. For the first time, we demonstrate that in-context learning (ICL) alone, without any gradient-based fine-tuning, can successfully tackle unseen Gymnasium tasks through imitation learning, online RL, or offline RL. Additionally, we show that achieving generalized ICRL capabilities-unlike task identification-oriented few-shot learning-critically depends on long trajectories generated by variant tasks and diverse behavior policies. By emphasizing the potential of ICL and departing from pre-training focused on acquiring specific skills, we further underscore the significance of meta-training aimed at cultivating the ability of ICL itself.

We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.

Stochastic approximation (SA) algorithms, first introduced by Robbins and Monro in the 1950's [24], has become one of the most important classes of stochastic numerical methods. Originally aimed at finding the the root of a continuous function given noisy observations, SA is now a fundamental tool in a range of areas such as statistics, optimization, electrical engineering, and machine learning, to mention but a few. Within the latter, the importance of SA algorithms is illustrated by the fact that a specific subclass of methods--stochastic gradient descent (SGD) methods--is central to the training of deep learning methods, and in reinforcement learning the standard methods (Q-learning and temporal-difference-learning) are variants of SA. The general class that is SA algorithms with state-dependent noise (see below for the definition) therefore constitute a rich and important family of stochastic recursive algorithms. In addition to the examples already mentioned (SGD, reinforcement learning), this class also includes persistent contrastive divergence, adaptive Markov chain Monte-Carlo (MCMC) and extended ensemble algorithms such as the Wang-Landau algorithm. The theory of SA stems from the pioneering work of Robbins and Monro [24] and Kiefer and Wolfowitz [20], and remains an active research area within probability theory. This is in part due to the many and diverse applications of SA algorithms where, due to the complex nature of the systems under considerations, different variants of the original Robbins-Monro algorithm are needed. In turn, developing the theoretical foundation for SA algorithms, such as, e.g., convergence results, central limit theorems, concentration results and results on deviations, is of fundamental importance; monographs covering many of the standard results of

In reinforcement learning (RL), agents often struggle to perform well on tasks that differ from those encountered during training. This limitation presents a challenge to the broader deployment of RL in diverse and dynamic task settings. In this work, we introduce memory augmentation, a memory-based RL approach to improve task generalization. Our approach leverages task-structured augmentations to simulate plausible out-of-distribution scenarios and incorporates memory mechanisms to enable context-aware policy adaptation. Trained on a predefined set of tasks, our policy demonstrates the ability to generalize to unseen tasks through memory augmentation without requiring additional interactions with the environment. Through extensive simulation experiments and real-world hardware evaluations on legged locomotion tasks, we demonstrate that our approach achieves zero-shot generalization to unseen tasks while maintaining robust in-distribution performance and high sample efficiency.

Standard reinforcement learning (RL) assumes that an agent can observe a reward for each state-action pair. However, in practical applications, it is often difficult and costly to collect a reward for each state-action pair. While there have been several works considering RL with trajectory feedback, it is unclear if trajectory feedback is inefficient for learning when trajectories are long. In this work, we consider a model named RL with segment feedback, which offers a general paradigm filling the gap between per-state-action feedback and trajectory feedback. In this model, we consider an episodic Markov decision process (MDP), where each episode is divided into $m$ segments, and the agent observes reward feedback only at the end of each segment. Under this model, we study two popular feedback settings: binary feedback and sum feedback, where the agent observes a binary outcome and a reward sum according to the underlying reward function, respectively. To investigate the impact of the number of segments $m$ on learning performance, we design efficient algorithms and establish regret upper and lower bounds for both feedback settings. Our theoretical and experimental results show that: under binary feedback, increasing the number of segments $m$ decreases the regret at an exponential rate; in contrast, surprisingly, under sum feedback, increasing $m$ does not reduce the regret significantly.

Large Language Models (LLMs) have shown remarkable potential in reasoning while they still suffer from severe factual hallucinations due to timeliness, accuracy, and coverage of parametric knowledge. Meanwhile, integrating reasoning with retrieval-augmented generation (RAG) remains challenging due to ineffective task decomposition and redundant retrieval, which can introduce noise and degrade response quality. In this paper, we propose DeepRAG, a framework that models retrieval-augmented reasoning as a Markov Decision Process (MDP), enabling strategic and adaptive retrieval. By iteratively decomposing queries, DeepRAG dynamically determines whether to retrieve external knowledge or rely on parametric reasoning at each step. Experiments show that DeepRAG improves retrieval efficiency while improving answer accuracy by 21.99%, demonstrating its effectiveness in optimizing retrieval-augmented reasoning.

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.