Learning a compact representation of history is critical for planning and generalization in partially observable environments. While meta-reinforcement learning (RL) agents can attain near Bayes-optimal policies, they often fail to learn the compact, interpretable Bayes-optimal belief states. This representational inefficiency potentially limits the agent's adaptability and generalization capacity. Inspired by predictive coding in neuroscience--which suggests that the brain predicts sensory inputs as a neural implementation of Bayesian inference--and by auxiliary predictive objectives in deep RL, we investigate whether integrating self-supervised predictive coding modules into meta-RL can facilitate learning of Bayes-optimal representations. Through state machine simulation, we show that meta-RL with predictive modules consistently generates more interpretable representations that better approximate Bayes-optimal belief states compared to conventional meta-RL across a wide variety of tasks, even when both achieve optimal policies. In challenging tasks requiring active information seeking, only meta-RL with predictive modules successfully learns optimal representations and policies, whereas conventional meta-RL struggles with inadequate representation learning. Finally, we demonstrate that better representation learning leads to improved generalization. Our results strongly suggest the role of predictive learning as a guiding principle for effective representation learning in agents navigating partial observability.

We study deployment-efficient reward-free exploration with linear function approximation, where the goal is to explore a linear Markov Decision Process (MDP) without revealing the reward function, while minimizing the number of distinct policies implemented during learning. By "deployment efficient", we mean algorithms that require few policies deployed during exploration - crucial in real-world applications where such deployments are costly or disruptive. We design a novel reinforcement learning algorithm that achieves near-optimal deployment efficiency for linear MDPs in the reward-free setting, using at most H exploration policies during execution (where H is the horizon length), while maintaining sample complexity polynomial in feature dimension and horizon length. Unlike previous approaches with similar deployment efficiency guarantees, our algorithm's sample complexity is independent of the reachability or explorability coefficients of the underlying MDP, which can be arbitrarily small and lead to unbounded sample complexity in certain cases - directly addressing an open problem from prior work. Our technical contributions include a data-dependent method for truncating stateaction pairs in linear MDPs, efficient offline policy evaluation and optimization algorithms for these truncated MDPs, and a careful integration of these components to implement reward-free exploration with linear function approximation without sacrificing deployment efficiency.

Reinforcement learning (RL) systems have countless applications, from energygrid management to protein design. However, such real-world scenarios are often extremely difficult, combinatorial in nature, and require complex coordination between multiple agents. This level of complexity can cause even state-of-theart RL systems, trained until convergence, to hit a performance ceiling which they are unable to break out of with zero-shot inference. Meanwhile, many digital or simulation-based applications allow for an inference phase that utilises a specific time and compute budget to explore multiple attempts before outputting a final solution. In this work, we show that such an inference phase employed at execution time, and the choice of a corresponding inference strategy, are key to breaking the performance ceiling observed in complex multi-agent RL problems. Our main result is striking: we can obtain up to a 126% and, on average, a 45% improvement over the previous state-of-the-art across 17 tasks, using only a couple seconds of extra wall-clock time during execution. We also demonstrate promising compute scaling properties, supported by over 60k experiments, making it the largest study on inference strategies for complex RL to date.

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence length. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem and solve for the fixed-point using a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. In several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. Additionally, we develop two new parallel quasi-Newton methods to evaluate nonlinear recursions with lower memory costs and reduced runtime. We find that the proposed parallel algorithms accelerate MCMC sampling across multiple examples, in some cases by more than an order of magnitude compared to sequential evaluation.

Biological brains demonstrate complex neural activity, where neural dynamics are critical to how brains process information. Most artificial neural networks ignore the complexity of individual neurons .

In this paper, we consider the general stochastic non-convex optimization problem when the sampling process follows a Markov chain. This problem exhibits its significance in capturing many real-world applications, ranging from asynchronous distributed learning to reinforcement learning. In particular, we consider the worst case where one has no prior knowledge and control of the Markov chain, meaning multiple trajectories cannot be simulated but only a single trajectory is available for algorithm design. We first provide algorithm-independent lower bounds with Ω(ϵ 3) (and Ω(ϵ 4)) samples, when objectives are (mean-squared) smooth, for any first-order methods accessing bounded variance gradient oracles to achieve ϵ-approximate critical solutions of original problems. Then, we propose MarkovChain SPIDER (MaC-SPIDER), which leverages variance-reduced techniques, to achieve a O(ϵ 3) upper bound for mean-squared smooth objective functions. To the best of our knowledge, MaC-SPIDER is the first to achieve O(ϵ 3)complexity when sampling from a single Markovian trajectory. And our proposed lower bound concludes its (near) optimality.

In this work, we study γ-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG).

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels.

Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

Behavior cloning has shown promise for robot manipulation, but real-world demonstrations are costly to acquire at scale. While simulated data offers a scalable alternative, particularly with advances in automated demonstration generation, transferring policies to the real world is hampered by various simulation and real domain gaps. In this work, we propose a unified sim-and-real co-training framework for learning generalizable manipulation policies that primarily leverages simulation and only requires a few real-world demonstrations. Central to our approach is learning a domain-invariant, task-relevant feature space. Our key insight is that aligning the joint distributions of observations and their corresponding actions across domains provides a richer signal than aligning observations (marginals) alone. We achieve this by embedding an Optimal Transport (OT)-inspired loss within the co-training framework, and extend this to an Unbalanced OT framework to handle the imbalance between abundant simulation data and limited real-world examples. We validate our method on challenging manipulation tasks, showing it can leverage abundant simulation data to achieve up to a 30% improvement in the real-world success rate and even generalize to scenarios seen only in simulation.