We reinterpret and propose a framework for pricing path-dependent financial derivatives by estimating the full distribution of payoffs using Distributional Reinforcement Learning (DistRL). Unlike traditional methods that focus on expected option value, our approach models the entire conditional distribution of payoffs, allowing for risk-aware pricing, tail-risk estimation, and enhanced uncertainty quantification. We demonstrate the efficacy of this method on Asian options, using quantile-based value function approximators.

The success of recent Artificial Intelligence (AI) models has been accompanied by the opacity of their internal mechanisms, due notably to the use of deep neural networks. In order to understand these internal mechanisms and explain the output of these AI models, a set of methods have been proposed, grouped under the domain of eXplainable AI (XAI). This paper focuses on a sub-domain of XAI, called eXplainable Reinforcement Learning (XRL), which aims to explain the actions of an agent that has learned by reinforcement learning. We propose an intuitive taxonomy based on two questions "What" and "How". The first question focuses on the target that the method explains, while the second relates to the way the explanation is provided. We use this taxonomy to provide a state-of-the-art review of over 250 papers. In addition, we present a set of domains close to XRL, which we believe should get attention from the community. Finally, we identify some needs for the field of XRL.

In the era of Large Language Models (LLMs), alignment has emerged as a fundamental yet challenging problem in the pursuit of more reliable, controllable, and capable machine intelligence. The recent success of reasoning models and conversational AI systems has underscored the critical role of reinforcement learning (RL) in enhancing these systems, driving increased research interest at the intersection of RL and LLM alignment. This paper provides a comprehensive review of recent advances in LLM alignment through the lens of inverse reinforcement learning (IRL), emphasizing the distinctions between RL techniques employed in LLM alignment and those in conventional RL tasks. In particular, we highlight the necessity of constructing neural reward models from human data and discuss the formal and practical implications of this paradigm shift. We begin by introducing fundamental concepts in RL to provide a foundation for readers unfamiliar with the field. We then examine recent advances in this research agenda, discussing key challenges and opportunities in conducting IRL for LLM alignment. Beyond methodological considerations, we explore practical aspects, including datasets, benchmarks, evaluation metrics, infrastructure, and computationally efficient training and inference techniques. Finally, we draw insights from the literature on sparse-reward RL to identify open questions and potential research directions. By synthesizing findings from diverse studies, we aim to provide a structured and critical overview of the field, highlight unresolved challenges, and outline promising future directions for improving LLM alignment through RL and IRL techniques.

We introduce a new framework of episodic tabular Markov decision processes (MDPs) with adversarial preferences, which we refer to as preference-based MDPs (PbMDPs). Unlike standard episodic MDPs with adversarial losses, where the numerical value of the loss is directly observed, in PbMDPs the learner instead observes preferences between two candidate arms, which represent the choices being compared. In this work, we focus specifically on the setting where the reward functions are determined by Borda scores. We begin by establishing a regret lower bound for PbMDPs with Borda scores. As a preliminary step, we present a simple instance to prove a lower bound of $Ω(\sqrt{HSAT})$ for episodic MDPs with adversarial losses, where $H$ is the number of steps per episode, $S$ is the number of states, $A$ is the number of actions, and $T$ is the number of episodes. Leveraging this construction, we then derive a regret lower bound of $Ω( (H^2 S K)^{1/3} T^{2/3} )$ for PbMDPs with Borda scores, where $K$ is the number of arms. Next, we develop algorithms that achieve a regret bound of order $T^{2/3}$. We first propose a global optimization approach based on online linear optimization over the set of all occupancy measures, achieving a regret bound of $\tilde{O}((H^2 S^2 K)^{1/3} T^{2/3} )$ under known transitions. However, this approach suffers from suboptimal dependence on the potentially large number of states $S$ and computational inefficiency. To address this, we propose a policy optimization algorithm whose regret is roughly bounded by $\tilde{O}( (H^6 S K^5)^{1/3} T^{2/3} )$ under known transitions, and further extend the result to the unknown-transition setting.

Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design options for optimal performance can be cumbersome, especially in modern computing environments: numerous different classical iterations and their variants exist, each with non-trivial per-step cost and tuning parameters. To this end, we propose MatRL -- a reinforcement learning based framework that automatically discovers iterative algorithms for computing matrix functions. The key idea is to treat algorithm design as a sequential decision-making process. Monte-Carlo tree search is then used to plan a hybrid sequence of matrix iterations and step sizes, tailored to a specific input matrix distribution and computing environment. Moreover, we also show that the learned algorithms provably generalize to sufficiently large matrices drawn from the same distribution. Finally, we corroborate our theoretical results with numerical experiments demonstrating that MatRL produces algorithms that outperform various baselines in the literature.

Scaling deep neural networks (NN) of reinforcement learning (RL) algorithms has been shown to enhance performance when feature extraction networks are used but the gained performance comes at the significant expense of increased computational and memory complexity. Neural network pruning methods have successfully addressed this challenge in supervised learning. However, their application to RL is underexplored. We propose an approach to integrate simultaneous training and pruning within advanced RL methods, in particular to RL algorithms enhanced by the Online Feature Extractor Network (OFENet). Our networks (XiNet) are trained to solve stochastic optimization problems over the RL networks' weights and the parameters of variational Bernoulli distributions for 0/1 Random Variables $ξ$ scaling each unit in the networks. The stochastic problem formulation induces regularization terms that promote convergence of the variational parameters to 0 when a unit contributes little to the performance. In this case, the corresponding structure is rendered permanently inactive and pruned from its network. We propose a cost-aware, sparsity-promoting regularization scheme, tailored to the DenseNet architecture of OFENets expressing the parameter complexity of involved networks in terms of the parameters of the RVs in these networks. Then, when matching this cost with the regularization terms, the many hyperparameters associated with them are automatically selected, effectively combining the RL objectives and network compression. We evaluate our method on continuous control benchmarks (MuJoCo) and the Soft Actor-Critic RL agent, demonstrating that OFENets can be pruned considerably with minimal loss in performance. Furthermore, our results confirm that pruning large networks during training produces more efficient and higher performing RL agents rather than training smaller networks from scratch.

In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The premise of our study is twofold: firstly, the further two states are from each other, transition-wise, the less relevant the value of the first state is when learning the $ε$-optimal value of the second; secondly, the amount of 'effort', sample-complexity-wise, expended in learning the $ε$-optimal value of a state is independent of the number of samples required to learn the $ε$-optimal value of a second state that is a sufficient number of transitions away from the first. Inversely, states within each other's vicinity have values that are dependent on each other and will require a similar number of samples to learn. By approximating the original MDP using smaller MDPs constructed using subsets of the original's state-space, we are able to reduce the sample-complexity by a logarithmic factor to $O(SA \log A)$ timesteps, where $S$ and $A$ are the state and action space sizes. We are able to extend these results to an infinite-horizon, model-free setting by constructing a PAC-MDP algorithm with the aforementioned sample-complexity. We conclude with showing how significant the improvement is by comparing our algorithm against prior work in an experimental setting.

The epidemic failure of replicability across empirical science and machine learning has recently motivated the formal study of replicable learning algorithms [Impagliazzo et al. (2022)]. In batch settings where data comes from a fixed i.i.d. source (e.g., hypothesis testing, supervised learning), the design of data-efficient replicable algorithms is now more or less understood. In contrast, there remain significant gaps in our knowledge for control settings like reinforcement learning where an agent must interact directly with a shifting environment. Karbasi et. al show that with access to a generative model of an environment with $S$ states and $A$ actions (the RL 'batch setting'), replicably learning a near-optimal policy costs only $\tilde{O}(S^2A^2)$ samples. On the other hand, the best upper bound without a generative model jumps to $\tilde{O}(S^7 A^7)$ [Eaton et al. (2024)] due to the substantial difficulty of environment exploration. This gap raises a key question in the broader theory of replicability: Is replicable exploration inherently more expensive than batch learning? Is sample-efficient replicable RL even possible? In this work, we (nearly) resolve this problem (for low-horizon tabular MDPs): exploration is not a significant barrier to replicable learning! Our main result is a replicable RL algorithm on $\tilde{O}(S^2A)$ samples, bridging the gap between the generative and episodic settings. We complement this with a matching $\tildeΩ(S^2A)$ lower bound in the generative setting (under the common parallel sampling assumption) and an unconditional lower bound in the episodic setting of $\tildeΩ(S^2)$ showcasing the near-optimality of our algorithm with respect to the state space $S$.

Can we acknowledge that our relationship with nature has evolved from human dominance to an intimate interconnectedness, recognizing that nature has genuinely attained a form of "personhood," and that artificial intelligence (AI) can facilitate this transforma - tion, serving as a novel medium for human-nature connection? This article begins by examining the critical role of AI at the heart of the urgent ecological transformation currently underway, exploring the paradigm shift emerging from the intersection of AI and non-human life. The discussion progressively narrows its focus to how this innovative AI-nature paradigm manifests specifically within the fields of art and design, highlighting its distinctiveness from traditional artistic and design media. The article seeks to explore how various artists and designers incorporate AI into ecological, microbiological, and geophysical creative practices. Through a comparative analysis of their creative strategies, it elaborates on the relationship between different applications of AI--such as data analysis, image recognition, and ecological restoration--and their unique artistic expressions, while also considering the extended value inherent in AI-driven art and design. However, the precise value of this emergent design paradigm remains subject to ongoing discourse.

Humanoid robots have seen remarkable advances in dexterity, balance, and locomotion, yet their role in expressive domains such as music performance remains largely unexplored. Musical tasks, like drumming, present unique challenges, including split-second timing, rapid contacts, and multi-limb coordination over performances lasting minutes. In this paper, we introduce Robot Drummer, a humanoid capable of expressive, high-precision drumming across a diverse repertoire of songs. We formulate humanoid drumming as sequential fulfillment of timed contacts and transform drum scores into a Rhythmic Contact Chain. To handle the long-horizon nature of musical performance, we decompose each piece into fixed-length segments and train a single policy across all segments in parallel using reinforcement learning. Through extensive experiments on over thirty popular rock, metal, and jazz tracks, our results demonstrate that Robot Drummer consistently achieves high F1 scores. The learned behaviors exhibit emergent human-like drumming strategies, such as cross-arm strikes, and adaptive stick assignments, demonstrating the potential of reinforcement learning to bring humanoid robots into the domain of creative musical performance. Project page: robotdrummer.github.io