Q-based Variational Inverse Reinforcement Learning

The development of safe and beneficial AI requires that systems can learn and act in accordance with human preferences. However, explicitly specifying these preferences by hand is often infeasible. Inverse reinforcement learning (IRL) addresses this challenge by inferring preferences, represented as reward functions, from expert behaviour. We introduce Q-based Variational IRL (QVIRL), a novel Bayesian IRL method that recovers a posterior distribution over rewards from expert demonstrations via primarily learning a variational distribution over optimal Q-values. Unlike previous approaches, QVIRL combines scalability with uncertainty quantification, important for safety-critical applications as well as active learning. We demonstrate QVIRL's strong performance in apprenticeship learning across various tasks, including gridworlds, Lunar Lander, the Highway Environment, and two ATARI games both with static expert data and with active learning. It is the first method for Bayesian IRL that demonstrates training from raw pixel observations.

Sound Probabilistic Safety Bounds for Large Language Models

We propose a novel framework for computing rigorous bounds on the probability that a large language model (LLM) generates harmful output to a given prompt. We study a new application of the Clopper-Pearson confidence intervals to obtain probably approximately correct (PAC) bounds for this problem. As our main technical contribution, we propose an algorithm that leverages features in the latent space to prioritize exploring branches in the auto-regressive generation tree that are more likely to produce harmful outputs. Our approach in particular enables the efficient computation of useful lower bounds, even in scenarios where the true harm probability is extremely small, and crucially, the obtained lower bounds are sound, i.e., formally proven to be less than the actual harmfulness probability: our experimental results demonstrate the effectiveness of our method by computing non-trivial lower bounds on state-of-the-art LLMs. This study newly enables the evaluation and statistical certification of LLMs.

Amortising Bayesian Experimental Design for Sequential Information Gathering in LLMs

Large language models (LLMs) exhibit strong reasoning and world-knowledge capabilities, yet often struggle to gather information effectively across the multi-turn interactions required in sequential decision-making settings. We introduce Amortised Sequential Information Gathering (ASIG), a fine-tuning approach that amortises Bayesian Experimental Design (BED) into LLM policies via a multi-turn extension of Group Relative Policy Optimisation with an Expected Information Gain reward. Evaluated on the 20 Questions task, ASIG more than doubles the success rate of the 7B base model and reduces inference cost by over $25\times$ relative to BED-LLM, a competitive inference-time baseline. Applied to MediQ, a medical diagnosis benchmark unseen during training, ASIG improves information-seeking performance at the 7B scale, suggesting that the learned strategies can transfer out of distribution. Our findings show that amortising BED into LLM policies provides an effective and computationally efficient approach to sequential information gathering.

Robust Shielding for Safe Reinforcement Learning

Shielding is an effective approach to formally guarantee the safety of reinforcement learning agents in Markov decision processes (MDPs). However, existing shielding techniques typically assume knowledge of the safety-relevant transition dynamics - a requirement that is seldom met in practice. To address this limitation, we introduce a novel shielding framework for robust MDPs (RMDPs), i.e., MDPs with sets of transition probabilities. We define safety as the satisfaction of a linear temporal logic (LTL) formula with a certain threshold probability under the worst-case transition probabilities of the RMDP. We prove that our shielding framework is both sound and optimal for the RMDP: every policy admissible by the shield is safe, and conversely, every safe RMDP policy is admissible by the shield. We combine our approach with existing sampling methods for learning transition probabilities of MDPs with probably approximately correct (PAC) guarantees. This combination enables the construction of shields for MDPs that, with high confidence, guarantee safety while remaining minimally restrictive. Our experiments show that our shields for learned RMDPs guarantee safety in unknown MDPs while recovering strong expected return as the number of samples increases.

Value Functions as Supermartingale Certificates

Certification methods for stochastic systems provide sufficient proof rules, based on real-valued supermartingale certificates, to determine the almost-sure satisfaction of $ω$-regular properties (and therefore of linear temporal logic) over general state spaces, encompassing both countably infinite and continuous state spaces. Conversely, reinforcement learning (RL) methods for $ω$-regular tasks have received considerable attention, but they typically lack formal guarantees that the learned policy satisfies the specification, except possibly for finite state and action spaces. We bridge these two lines of research by establishing a novel theoretical connection: under an appropriate reward, the value function associated to a policy that almost surely satisfies an $ω$-regular property encodes a Streett supermartingale certificate for that specification. Our results, validated experimentally on finite Markov decision processes, hold for finite, countably infinite, and continuous state spaces, suggesting a principled route to certificate synthesis via RL.

HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of over 100 predominantly unsolved problems spanning 8 domains in computational and applied mathematics, paired with an open-source evaluation framework for automated verification. Our benchmark targets a class of problems where discovery is hard, requiring meaningful mathematical insight, but verification is computationally efficient and simple. Because these solutions are unknown, HorizonMath is immune to data contamination, and most state-of-the-art models score near 0%. Existing research-level benchmarks instead rely on formal proof verification or manual review, both of which are expensive to scale. Using this platform, we find two problems for which GPT 5.4 Pro proposes solutions that improve on the best-known published results, representing potential novel contributions (pending expert review). We release HorizonMath as an open challenge and a growing community resource, where correct solutions to problems in the unsolved problem classes could constitute novel results in the mathematical literature.

When can we trust untrusted monitoring? A safety case sketch across collusion strategies

AIs are increasingly being deployed with greater autonomy and capabilities, which increases the risk that a misaligned AI may be able to cause catastrophic harm. Untrusted monitoring -- using one untrusted model to oversee another -- is one approach to reducing risk. Justifying the safety of an untrusted monitoring deployment is challenging because developers cannot safely deploy a misaligned model to test their protocol directly. In this paper, we develop upon existing methods for rigorously demonstrating safety based on pre-deployment testing. We relax assumptions that previous AI control research made about the collusion strategies a misaligned AI might use to subvert untrusted monitoring. We develop a taxonomy covering passive self-recognition, causal collusion (hiding pre-shared signals), acausal collusion (hiding signals via Schelling points), and combined strategies. We create a safety case sketch to clearly present our argument, explicitly state our assumptions, and highlight unsolved challenges. We identify conditions under which passive self-recognition could be a more effective collusion strategy than those studied previously. Our work builds towards more robust evaluations of untrusted monitoring.

Zero-Shot Instruction Following in RL via Structured LTL Representations

We study instruction following in multi-task reinforcement learning, where an agent must zero-shot execute novel tasks not seen during training. In this setting, linear temporal logic (LTL) has recently been adopted as a powerful framework for specifying structured, temporally extended tasks. While existing approaches successfully train generalist policies, they often struggle to effectively capture the rich logical and temporal structure inherent in LTL specifications. In this work, we address these concerns with a novel approach to learn structured task representations that facilitate training and generalisation. Our method conditions the policy on sequences of Boolean formulae constructed from a finite automaton of the task. We propose a hierarchical neural architecture to encode the logical structure of these formulae, and introduce an attention mechanism that enables the policy to reason about future subgoals. Experiments in a variety of complex environments demonstrate the strong generalisation capabilities and superior performance of our approach.

Semantically Labelled Automata for Multi-Task Reinforcement Learning with LTL Instructions

We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae, which are commonly used in formal methods to specify properties of systems, and have recently been successfully adopted in RL. In this setting, we present a novel task embedding technique leveraging a new generation of semantic LTL-to-automata translations, originally developed for temporal synthesis. The resulting semantically labelled automata contain rich, structured information in each state that allow us to (i) compute the automaton efficiently on-the-fly, (ii) extract expressive task embeddings used to condition the policy, and (iii) naturally support full LTL. Experimental results in a variety of domains demonstrate that our approach achieves state-of-the-art performance and is able to scale to complex specifications where existing methods fail.

Probabilistic Performance Guarantees for Multi-Task Reinforcement Learning

Multi-task reinforcement learning trains generalist policies that can execute multiple tasks. While recent years have seen significant progress, existing approaches rarely provide formal performance guarantees, which are indispensable when deploying policies in safety-critical settings. We present an approach for computing high-confidence guarantees on the performance of a multi-task policy on tasks not seen during training. Concretely, we introduce a new generalisation bound that composes (i) per-task lower confidence bounds from finitely many rollouts with (ii) task-level generalisation from finitely many sampled tasks, yielding a high-confidence guarantee for new tasks drawn from the same arbitrary and unknown distribution. Across state-of-the-art multi-task RL methods, we show that the guarantees are theoretically sound and informative at realistic sample sizes.