Sequential latent-variable models with subject-specific random effects provide a flexible framework for modeling temporally structured data with both local latent dynamics and stable between-subject heterogeneity. In such models, conditional inference for the local latent process is often tractable, but integrating over subject-specific random effects can be computationally demanding. We propose an anchored variational inference framework for efficient approximate inference in this setting. The central idea is to replace the full conditional posterior of the local latent process with its evaluation at a representative value of the subject-specific latent effect, called the anchor point, thereby preserving tractable local inference while substantially reducing computational cost. This approximation is especially appealing in sequential settings, where the posterior distribution of the random effect becomes increasingly concentrated as the sequence length grows. Under suitable conditions, we show that the posterior mean is a nearly optimal anchor point and that the resulting anchored variational EM (AVEM) algorithm approximately preserves the local monotonicity behavior of standard variational inference. We instantiate the framework in two representative classes of sequential latent-variable models, namely mixed hidden Markov models and mixed-effects state-space models, derive the corresponding AVEM algorithms, and use simulation studies to indicate that the resulting methods achieve accurate estimation with substantial computational gains. We also discuss a partially anchored variant of the framework, in which only the components of the subject-specific latent effect whose posteriors are well concentrated are anchored.

In-context learning (ICL) is one of the most powerful and most unexpected capabilities to emerge in recent transformer-based large language models (LLMs). Yet the mechanisms that underlie it are poorly understood. In this paper, we demonstrate that comparable ICL capabilities can be acquired by an alternative sequence prediction learning method, namely clone-structured causal graphs (CSCGs). A key property of CSCGs is that, unlike transformer-based LLMs, they are interpretable, which considerably simplifies the task of explaining how ICL works. We show that ICL in CSCG uses a combination of (a) learning template (schema) circuits for pattern completion, (b) retrieving relevant templates in a context-sensitive manner, and (c) rebinding novel tokens to appropriate slots in the templates. We go on to marshall evidence for the hypothesis that similar mechanisms underlie ICL in LLMs. For example, we find that, with CSCGs as with LLMs, different capabilities emerge at different levels of overparameterization, suggesting that overparameterization helps in learning more complex template (schema) circuits. By showing how ICL can be achieved with small models and datasets, we open up a path to novel architectures, and take a vital step towards a more general understanding of the mechanics behind this important capability.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously.

Multi-agent reinforcement learning (MARL) has witnessed significant progress with the development of value function factorization methods. It allows optimizing a joint action-value function through the maximization of factorized per-agent utilities. In this paper, we show that in partially observable MARL problems, an agent's ordering over its own actions could impose concurrent constraints (across different states) on the representable function class, causing significant estimation errors during training. We tackle this limitation and propose PAC, a new framework leveraging Assistive information generated from Counterfactual Predictions of optimal joint action selection, which enable explicit assistance to value function factorization through a novel counterfactual loss. A variational inference-based information encoding method is developed to collect and encode the counterfactual predictions from an estimated baseline. To enable decentralized execution, we also derive factorized per-agent policies inspired by a maximum-entropy MARL framework. We evaluate the proposed PAC on multi-agent predator-prey and a set of StarCraft II micromanagement tasks. Empirical results demonstrate improved results of PAC over state-of-the-art value-based and policy-based multi-agent reinforcement learning algorithms on all benchmarks.

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon H with S states, and A actions. The performance of an agent is measured by the regret after interacting with the environment for T episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in H, S, A, and T per state-action pair.

We propose a novel approach to interactive theorem proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We formulate the process of ITP as a Markov decision process (MDP) in which each state represents a set of potential derivation paths. This structure allows us to introduce a search mechanism which enables the agent to efficiently discard (predicted) dead-end derivations and restart from promising alternatives. We implement the framework in the HOL4 theorem prover. Experimental results show that the framework using learned search strategies outperforms existing automated theorem provers (i.e.