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Recently regular decision processes have been proposed as a well-behaved form of non-Markov decision process. Regular decision processes are characterised by a transition function and a reward function that depend on the whole history,…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
Reinforcement learning (RL) -- algorithms that teach artificial agents to interact with environments by maximising reward signals -- has achieved significant success in recent years. These successes have been facilitated by advances in…
This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
We study risk-sensitive reinforcement learning in finite discounted MDPs, where a generative model of the MDP is assumed to be available. We consider a family or risk measures called the optimized certainty equivalent (OCE), which includes…
Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such…
Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…
We investigate the Probably Approximately Correct (PAC) property of scenario decision algorithms, which refers to their ability to produce decisions with an arbitrarily low risk of violating unknown safety constraints, provided a sufficient…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
We study the computational relationship between replicability (Impagliazzo et al. [STOC `22], Ghazi et al. [NeurIPS `21]) and other stability notions. Specifically, we focus on replicable PAC learning and its connections to differential…
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating…
Reinforcement learning with outcome-based feedback faces a fundamental challenge: when rewards are only observed at trajectory endpoints, how do we assign credit to the right actions? This paper provides the first comprehensive analysis of…
We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch…
In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects of supervised, unsupervised and reinforcement learning. Reinforcement learning offers numerous…
When data is scarce or mistakes are costly, average-case metrics fall short. What a practitioner needs is a guarantee: with probability at least $1-\delta$, the learned policy is $\varepsilon$-close to optimal after $N$ episodes. This is…
The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…