In recent years, the impact of machine learning (ML) and artificial intelligence (AI) in society has been absolutely remarkable. This impact is expected to continue in the foreseeable future. However,the adoption of AI/ML is also a cause of grave concern. The operation of the most advances AI/ML models is often beyond the grasp of human decision makers. As a result, decisions that impact humans may not be understood and may lack rigorous validation. Explainable AI (XAI) is concerned with providing human decision-makers with understandable explanations for the predictions made by ML models. As a result, XAI is a cornerstone of trustworthy AI. Despite its strategic importance, most work on XAI lacks rigor, and so its use in high-risk or safety-critical domains serves to foster distrust instead of contributing to build much-needed trust. Logic-based XAI has recently emerged as a rigorous alternative to those other non-rigorous methods of XAI. This paper provides a technical survey of logic-based XAI, its origins, the current topics of research, and emerging future topics of research. The paper also highlights the many myths that pervade non-rigorous approaches for XAI.

Recent works have studied *state entropy maximization* in reinforcement learning, in which the agent's objective is to learn a policy inducing high entropy over states visitation (Hazan et al., 2019). They typically assume full observability of the state of the system, so that the entropy of the observations is maximized. In practice, the agent may only get *partial* observations, e.g., a robot perceiving the state of a physical space through proximity sensors and cameras. A significant mismatch between the entropy over observations and true states of the system can arise in those settings. In this paper, we address the problem of entropy maximization over the *true states* with a decision policy conditioned on partial observations *only*. The latter is a generalization of POMDPs, which is intractable in general. We develop a memory and computationally efficient *policy gradient* method to address a first-order relaxation of the objective defined on *belief* states, providing various formal characterizations of approximation gaps, the optimization landscape, and the *hallucination* problem. This paper aims to generalize state entropy maximization to more realistic domains that meet the challenges of applications.

In this paper, we study safe data collection for the purpose of policy evaluation in tabular Markov decision processes (MDPs). In policy evaluation, we are given a \textit{target} policy and asked to estimate the expected cumulative reward it will obtain. Policy evaluation requires data and we are interested in the question of what \textit{behavior} policy should collect the data for the most accurate evaluation of the target policy. While prior work has considered behavior policy selection, in this paper, we additionally consider a safety constraint on the behavior policy. Namely, we assume there exists a known default policy that incurs a particular expected cost when run and we enforce that the cumulative cost of all behavior policies ran is better than a constant factor of the cost that would be incurred had we always run the default policy. We first show that there exists a class of intractable MDPs where no safe oracle algorithm with knowledge about problem parameters can efficiently collect data and satisfy the safety constraints. We then define the tractability condition for an MDP such that a safe oracle algorithm can efficiently collect data and using that we prove the first lower bound for this setting. We then introduce an algorithm SaVeR for this problem that approximates the safe oracle algorithm and bound the finite-sample mean squared error of the algorithm while ensuring it satisfies the safety constraint. Finally, we show in simulations that SaVeR produces low MSE policy evaluation while satisfying the safety constraint.

We address the challenge of quantifying Bayesian uncertainty and incorporating it in offline use cases of finite-state Markov Decision Processes (MDPs) with unknown dynamics. Our approach provides a principled method to disentangle epistemic and aleatoric uncertainty, and a novel technique to find policies that optimise Bayesian posterior expected value without relying on strong assumptions about the MDP's posterior distribution. First, we utilise standard Bayesian reinforcement learning methods to capture the posterior uncertainty in MDP parameters based on available data. We then analytically compute the first two moments of the return distribution across posterior samples and apply the law of total variance to disentangle aleatoric and epistemic uncertainties. To find policies that maximise posterior expected value, we leverage the closed-form expression for value as a function of policy. This allows us to propose a stochastic gradient-based approach for solving the problem. We illustrate the uncertainty quantification and Bayesian posterior value optimisation performance of our agent in simple, interpretable gridworlds and validate it through ground-truth evaluations on synthetic MDPs. Finally, we highlight the real-world impact and computational scalability of our method by applying it to the AI Clinician problem, which recommends treatment for patients in intensive care units and has emerged as a key use case of finite-state MDPs with offline data. We discuss the challenges that arise with Bayesian modelling of larger scale MDPs while demonstrating the potential to apply our methods rooted in Bayesian decision theory into the real world. We make our code available at https://github.com/filippovaldettaro/finite-state-mdps .

Sequential modeling has demonstrated remarkable capabilities in offline reinforcement learning (RL), with Decision Transformer (DT) being one of the most notable representatives, achieving significant success. However, RL trajectories possess unique properties to be distinguished from the conventional sequence (e.g., text or audio): (1) local correlation, where the next states in RL are theoretically determined solely by current states and actions based on the Markov Decision Process (MDP), and (2) global correlation, where each step's features are related to long-term historical information due to the time-continuous nature of trajectories. In this paper, we propose a novel action sequence predictor, named Mamba Decision Maker (MambaDM), where Mamba is expected to be a promising alternative for sequence modeling paradigms, owing to its efficient modeling of multi-scale dependencies. In particular, we introduce a novel mixer module that proficiently extracts and integrates both global and local features of the input sequence, effectively capturing interrelationships in RL datasets. Extensive experiments demonstrate that MambaDM achieves state-of-the-art performance in Atari and OpenAI Gym datasets. Furthermore, we empirically investigate the scaling laws of MambaDM, finding that increasing model size does not bring performance improvement, but scaling the dataset amount by 2x for MambaDM can obtain up to 33.7% score improvement on Atari dataset. This paper delves into the sequence modeling capabilities of MambaDM in the RL domain, paving the way for future advancements in robust and efficient decision-making systems. Our code will be available at https://github.com/AndyCao1125/MambaDM.

The pursuit of high perceptual quality in image restoration has driven the development of revolutionary generative models, capable of producing results often visually indistinguishable from real data. However, as their perceptual quality continues to improve, these models also exhibit a growing tendency to generate hallucinations - realistic-looking details that do not exist in the ground truth images. The presence of hallucinations introduces uncertainty regarding the reliability of the models' predictions, raising major concerns about their practical application. In this paper, we employ information-theory tools to investigate this phenomenon, revealing a fundamental tradeoff between uncertainty and perception. We rigorously analyze the relationship between these two factors, proving that the global minimal uncertainty in generative models grows in tandem with perception. In particular, we define the inherent uncertainty of the restoration problem and show that attaining perfect perceptual quality entails at least twice this uncertainty. Additionally, we establish a relation between mean squared-error distortion, uncertainty and perception, through which we prove the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff. This work uncovers fundamental limitations of generative models in achieving both high perceptual quality and reliable predictions for image restoration. We demonstrate our theoretical findings through an analysis of single image super-resolution algorithms. Our work aims to raise awareness among practitioners about this inherent tradeoff, empowering them to make informed decisions and potentially prioritize safety over perceptual performance.

Meta reinforcement learning sets a distribution over a set of tasks on which the agent can train at will, then is asked to learn an optimal policy for any test task efficiently. In this paper, we consider a finite set of tasks modeled through Markov decision processes with various dynamics. We assume to have endured a long training phase, from which the set of tasks is perfectly recovered, and we focus on regret minimization against the optimal policy in the unknown test task. Under a separation condition that states the existence of a state-action pair revealing a task against another, Chen et al. (2022) show that $O(M^2 \log(H))$ regret can be achieved, where $M, H$ are the number of tasks in the set and test episodes, respectively. In our first contribution, we demonstrate that the latter rate is nearly optimal by developing a novel lower bound for test-time regret minimization under separation, showing that a linear dependence with $M$ is unavoidable. Then, we present a family of stronger yet reasonable assumptions beyond separation, which we call strong identifiability, enabling algorithms achieving fast rates $\log (H)$ and sublinear dependence with $M$ simultaneously. Our paper provides a new understanding of the statistical barriers of test-time regret minimization and when fast rates can be achieved.

Estimating the uncertainty of a model's prediction on a test point is a crucial part of ensuring reliability and calibration under distribution shifts. A minimum description length approach to this problem uses the predictive normalized maximum likelihood (pNML) distribution, which considers every possible label for a data point, and decreases confidence in a prediction if other labels are also consistent with the model and training data. In this work we propose IF-COMP, a scalable and efficient approximation of the pNML distribution that linearizes the model with a temperature-scaled Boltzmann influence function. IF-COMP can be used to produce well-calibrated predictions on test points as well as measure complexity in both labelled and unlabelled settings. We experimentally validate IF-COMP on uncertainty calibration, mislabel detection, and OOD detection tasks, where it consistently matches or beats strong baseline methods.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the (indefinite-horizon) Maximal Reachability Probability Problem (MRPP), where the goal is to maximize the probability of reaching some target states. This is also a core problem in model checking with logical specifications and is naturally undiscounted (discount factor is one). Inspired by the success of point-based methods developed for discounted problems, we study their extensions to MRPP. Specifically, we focus on trial-based heuristic search value iteration techniques and present a novel algorithm that leverages the strengths of these techniques for efficient exploration of the belief space (informed search via value bounds) while addressing their drawbacks in handling loops for indefinite-horizon problems. The algorithm produces policies with two-sided bounds on optimal reachability probabilities. We prove convergence to an optimal policy from below under certain conditions. Experimental evaluations on a suite of benchmarks show that our algorithm outperforms existing methods in almost all cases in both probability guarantees and computation time.