Conformal prediction (CP) is a popular frequentist framework for representing uncertainty by providing prediction sets that guarantee coverage of the true label with a user-adjustable probability. In most applications, CP operates on confidence scores coming from a standard (first-order) probabilistic predictor (e.g., softmax outputs). Second-order predictors, such as credal set predictors or Bayesian models, are also widely used for uncertainty quantification and are known for their ability to represent both aleatoric and epistemic uncertainty. Despite their popularity, there is still an open question on ``how they can be incorporated into CP''. In this paper, we discuss the desiderata for CP when valid second-order predictions are available. We then introduce Bernoulli prediction sets (BPS), which produce the smallest prediction sets that ensure conditional coverage in this setting. When given first-order predictions, BPS reduces to the well-known adaptive prediction sets (APS). Furthermore, when the validity assumption on the second-order predictions is compromised, we apply conformal risk control to obtain a marginal coverage guarantee while still accounting for epistemic uncertainty.

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of architecture, hyperparameters and optimization procedure. However, deploying deep learning models out-of-distribution, in sequential decision-making tasks, or in safety-critical domains, necessitates reliable uncertainty quantification, not just a point estimate. The machinery of modern approximate inference -- Bayesian deep learning -- should answer the need for uncertainty quantification, but its effectiveness has been challenged by our inability to define useful explicit inductive biases through priors, as well as the associated computational burden. Instead, in this work we demonstrate, both theoretically and empirically, how to regularize a variational deep network implicitly via the optimization procedure, just as for standard deep learning. We fully characterize the inductive bias of (stochastic) gradient descent in the case of an overparametrized linear model as generalized variational inference and demonstrate the importance of the choice of parametrization. Finally, we show empirically that our approach achieves strong in- and out-of-distribution performance without tuning of additional hyperparameters and with minimal time and memory overhead over standard deep learning.

This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure children per latent variable or restrictions on the latent causal graph. Furthermore, it is common for all observed variables to exhibit the same modality. Consequently, the existing identifiability conditions are often too stringent for complex real-world data. We consider a general nonparametric measurement model with arbitrary observed variable types and binary latent variables, and propose a double triangular graphical condition that guarantees identifiability of the entire causal graphical model. The proposed condition significantly relaxes the popular pure children condition. We also establish necessary conditions for identifiability and provide valuable insights into fundamental limits of identifiability. Simulation studies verify that latent structures satisfying our conditions can be accurately estimated from data.

The softmax-contaminated mixture of experts (MoE) model is deployed when a large-scale pre-trained model, which plays the role of a fixed expert, is fine-tuned for learning downstream tasks by including a new contamination part, or prompt, functioning as a new, trainable expert. Despite its popularity and relevance, the theoretical properties of the softmax-contaminated MoE have remained unexplored in the literature. In the paper, we study the convergence rates of the maximum likelihood estimator of gating and prompt parameters in order to gain insights into the statistical properties and potential challenges of fine-tuning with a new prompt. We find that the estimability of these parameters is compromised when the prompt acquires overlapping knowledge with the pre-trained model, in the sense that we make precise by formulating a novel analytic notion of distinguishability. Under distinguishability of the pre-trained and prompt models, we derive minimax optimal estimation rates for all the gating and prompt parameters. By contrast, when the distinguishability condition is violated, these estimation rates become significantly slower due to their dependence on the prompt convergence rate to the pre-trained model. Finally, we empirically corroborate our theoretical findings through several numerical experiments.

Actor-Critic methods are widely used for their scalability, yet existing theoretical guarantees for infinite-horizon average-reward Markov Decision Processes (MDPs) often rely on restrictive ergodicity assumptions. We propose NAC-B, a Natural Actor-Critic with Batching, that achieves order-optimal regret of $\tilde{O}(\sqrt{T})$ in infinite-horizon average-reward MDPs under the unichain assumption, which permits both transient states and periodicity. This assumption is among the weakest under which the classic policy gradient theorem remains valid for average-reward settings. NAC-B employs function approximation for both the actor and the critic, enabling scalability to problems with large state and action spaces. The use of batching in our algorithm helps mitigate potential periodicity in the MDP and reduces stochasticity in gradient estimates, and our analysis formalizes these benefits through the introduction of the constants $C_{\text{hit}}$ and $C_{\text{tar}}$, which characterize the rate at which empirical averages over Markovian samples converge to the stationary distribution.

We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski's equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods - an uncommon feature among scalable methods - makes our approach particularly suited for model selection, which we validate through dedicated experiments.

Meta-reinforcement learning trains a single reinforcement learning agent on a distribution of tasks to quickly generalize to new tasks outside of the training set at test time. From a Bayesian perspective, one can interpret this as performing amortized variational inference on the posterior distribution over training tasks. Among the various meta-reinforcement learning approaches, a common method is to represent this distribution with a point-estimate using a recurrent neural network. We show how one can augment this point estimate to give full distributions through the Laplace approximation, either at the start of, during, or after learning, without modifying the base model architecture. With our approximation, we are able to estimate distribution statistics (e.g., the entropy) of non-Bayesian agents and observe that point-estimate based methods produce overconfident estimators while not satisfying consistency. Furthermore, when comparing our approach to full-distribution based learning of the task posterior, our method performs on par with variational baselines while having much fewer parameters.

While AI agents hold transformative potential in business, effective performance benchmarking is hindered by the scarcity of public, realistic business data on widely used platforms. Existing benchmarks often lack fidelity in their environments, data, and agent-user interactions, with limited coverage of diverse business scenarios and industries. To address these gaps, we introduce CRMArena-Pro, a novel benchmark for holistic, realistic assessment of LLM agents in diverse professional settings. CRMArena-Pro expands on CRMArena with nineteen expert-validated tasks across sales, service, and 'configure, price, and quote' processes, for both Business-to-Business and Business-to-Customer scenarios. It distinctively incorporates multi-turn interactions guided by diverse personas and robust confidentiality awareness assessments. Experiments reveal leading LLM agents achieve only around 58% single-turn success on CRMArena-Pro, with performance dropping significantly to approximately 35% in multi-turn settings. While Workflow Execution proves more tractable for top agents (over 83% single-turn success), other evaluated business skills present greater challenges. Furthermore, agents exhibit near-zero inherent confidentiality awareness; though targeted prompting can improve this, it often compromises task performance. These findings highlight a substantial gap between current LLM capabilities and enterprise demands, underscoring the need for advancements in multi-turn reasoning, confidentiality adherence, and versatile skill acquisition.

With the recent success of world-model agents, which extend the core idea of model-based reinforcement learning by learning a differentiable model for sample-efficient control across diverse tasks, active inference (AIF) offers a complementary, neuroscience-grounded paradigm that unifies perception, learning, and action within a single probabilistic framework powered by a generative model. Despite this promise, practical AIF agents still rely on accurate immediate predictions and exhaustive planning, a limitation that is exacerbated in delayed environments requiring plans over long horizons, tens to hundreds of steps. Moreover, most existing agents are evaluated on robotic or vision benchmarks which, while natural for biological agents, fall short of real-world industrial complexity. We address these limitations with a generative-policy architecture featuring (i) a multi-step latent transition that lets the generative model predict an entire horizon in a single look-ahead, (ii) an integrated policy network that enables the transition and receives gradients of the expected free energy, (iii) an alternating optimization scheme that updates model and policy from a replay buffer, and (iv) a single gradient step that plans over long horizons, eliminating exhaustive planning from the control loop. We evaluate our agent in an environment that mimics a realistic industrial scenario with delayed and long-horizon settings. The empirical results confirm the effectiveness of the proposed approach, demonstrating the coupled world-model with the AIF formalism yields an end-to-end probabilistic controller capable of effective decision making in delayed, long-horizon settings without handcrafted rewards or expensive planning.

Multi-Agent Reinforcement Learning (MARL) has shown great potential as an adaptive solution for addressing modern cybersecurity challenges. MARL enables decentralized, adaptive, and collaborative defense strategies and provides an automated mechanism to combat dynamic, coordinated, and sophisticated threats. This survey investigates the current state of research in MARL applications for automated cyber defense (ACD), focusing on intruder detection and lateral movement containment. Additionally, it examines the role of Autonomous Intelligent Cyber-defense Agents (AICA) and Cyber Gyms in training and validating MARL agents. Finally, the paper outlines existing challenges, such as scalability and adversarial robustness, and proposes future research directions. This also discusses how MARL integrates in AICA to provide adaptive, scalable, and dynamic solutions to counter the increasingly sophisticated landscape of cyber threats. It highlights the transformative potential of MARL in areas like intrusion detection and lateral movement containment, and underscores the value of Cyber Gyms for training and validation of AICA.