Most reinforcement learning (RL) algorithms hinge on the Markovian assumption, i.e. that the underlying system transitions and rewards are Markovian in some natural notion of (observable)

Agent 1's action is resolved first. Figure 8: An example of Agent 1 using the "clean" action while facing East. The "main" beam extends directly in front of the agent, while two auxiliary A beam stops when it hits a dirty river tile. The Sequential Social Dilemma Games, introduced in Leibo et al. [2017], are a kind of MARL All of these have open source implementations in [Vinitsky et al., 2019]. The cleaning beam is shown in Figure 8a.

Existing online learning algorithms for adversarial Markov Decision Processes achieve $\mathcal{O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed.This is because it has been shown that adversarial transition functions make no-regret learning impossible.Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary.More concretely, we first propose an algorithm that enjoys $\widetilde{\mathcal{O}}(\sqrt{T} + C^{P})$ regret where $C^{P}$ measures how adversarial the transition functions are and can be at most $\mathcal{O}(T)$.While this algorithm itself requires knowledge of $C^{P}$, we further develop a black-box reduction approach that removes this requirement.Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in [Jin et al. 2021]) and achieves $\widetilde{\mathcal{O}}(U + \sqrt{UC^{L}} + C^{P})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{L}$ is the amount of corruption on losses.

In this paper we consider the problem of computing an $\epsilon$-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any state-action pair samples from the transition function in $O(1)$ time.

We consider online learning in episodic loop-free Markov decision processes (MDPs), where the loss function can change arbitrarily between episodes. The transition function is fixed but unknown to the learner, and the learner only observes bandit feedback (not the entire loss function). For this problem we develop no-regret algorithms that perform asymptotically as well as the best stationary policy in hindsight. Assuming that all states are reachable with probability $\beta > 0$ under any policy, we give a regret bound of $\tilde{O} ( L|X|\sqrt{|A|T} / \beta)$, where $T$ is the number of episodes, $X$ is the state space, $A$ is the action space, and $L$ is the length of each episode. When this assumption is removed we give a regret bound of $\tilde{O} ( L^{3/2} |X| |A|^{1/4} T^{3/4})$, that holds for an arbitrary transition function. To our knowledge these are the first algorithms that in our setting handle both bandit feedback and an unknown transition function.

Why do modern language models, trained to do well on next-word prediction, appear to generate coherent documents and capture long-range structure? Here we show that next-token prediction is provably powerful for learning longer-range structure, even with common neural network architectures. Specifically, we prove that optimizing next-token prediction over a Recurrent Neural Network (RNN) yields a model that closely approximates the training distribution: for held-out documents sampled from the training distribution, no algorithm of bounded description length limited to examining the next $k$ tokens, for any $k$, can distinguish between $k$ consecutive tokens of such documents and $k$ tokens generated by the learned language model following the same prefix. We provide polynomial bounds (in $k$, independent of the document length) on the model size needed to achieve such $k$-token indistinguishability, offering a complexity-theoretic explanation for the long-range coherence observed in practice.

Abstract-- T o support the circular economy, robotic systems must not only assemble new products but also disassemble end-of-life (EOL) ones for reuse, recycling, or safe disposal. Existing approaches to disassembly sequence planning often assume deterministic and fully observable product models, yet real EOL products frequently deviate from their initial designs due to wear, corrosion, or undocumented repairs. We argue that disassembly should therefore be formulated as a Partially Observable Markov Decision Process (POMDP), which naturally captures uncertainty about the product's internal state. We present a mathematical formulation of disassembly as a POMDP, in which hidden variables represent uncertain structural or physical properties. Building on this formulation, we propose a task and motion planning framework that automatically derives specific POMDP models from CAD data, robot capabilities, and inspection results. T o obtain tractable policies, we approximate this formulation with a reinforcement-learning approach that operates on stochastic action outcomes informed by inspection priors, while a Bayesian filter continuously maintains beliefs over latent EOL conditions during execution. Using three products on two robotic systems, we demonstrate that this probabilistic planning framework outperforms deterministic baselines in terms of average disassembly time and variance, generalizes across different robot setups, and successfully adapts to deviations from the CAD model, such as missing or stuck parts. I. INTRODUCTION Modern industrial production still follows a linear model of make-use-dispose, accelerating the depletion of natural resources on our planet.