In many real-world applications, agents must make sequential decisions in environments where conditions are subject to change due to various exogenous factors. These non-stationary environments pose significant challenges to traditional decision-making models, which typically assume stationary dynamics. Non-stationary Markov decision processes (NS-MDPs) offer a framework to model and solve decision problems under such changing conditions. However, the lack of standardized benchmarks and simulation tools has hindered systematic evaluation and advance in this field. We present NS-Gym, the first simulation toolkit designed explicitly for NS-MDPs, integrated within the popular Gymnasium framework. In NS-Gym, we segregate the evolution of the environmental parameters that characterize non-stationarity from the agent's decision-making module, allowing for modular and flexible adaptations to dynamic environments. We review prior work in this domain and present a toolkit encapsulating key problem characteristics and types in NS-MDPs. This toolkit is the first effort to develop a set of standardized interfaces and benchmark problems to enable consistent and reproducible evaluation of algorithms under non-stationary conditions. We also benchmark six algorithmic approaches from prior work on NS-MDPs using NS-Gym. Our vision is that NS-Gym will enable researchers to assess the adaptability and robustness of their decision-making algorithms to non-stationary conditions.

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities, practical applications in fields such as biology often require sample generation that maximizes specific metrics (e.g., stability, affinity in proteins, closeness to target structures). In these scenarios, diffusion models can be adapted not only to generate realistic samples but also to explicitly maximize desired measures at inference time without fine-tuning. This tutorial explores the foundational aspects of such inference-time algorithms. We review these methods from a unified perspective, demonstrating that current techniques -- such as Sequential Monte Carlo (SMC)-based guidance, value-based sampling, and classifier guidance -- aim to approximate soft optimal denoising processes (a.k.a. policies in RL) that combine pre-trained denoising processes with value functions serving as look-ahead functions that predict from intermediate states to terminal rewards. Within this framework, we present several novel algorithms not yet covered in the literature. Furthermore, we discuss (1) fine-tuning methods combined with inference-time techniques, (2) inference-time algorithms based on search algorithms such as Monte Carlo tree search, which have received limited attention in current research, and (3) connections between inference-time algorithms in language models and diffusion models. The code of this tutorial on protein design is available at https://github.com/masa-ue/AlignInversePro

We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure. The main challenge with learning parameters of such models is that iterative methods such as EM are very slow, while naive spectral methods result in time and space complexity exponential in the number of cell types. We exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets. We provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types.

In-context learning is a remarkable capability of transformers, referring to their ability to adapt to specific tasks based on a short history or context. Previous research has found that task-specific information is locally encoded within models, though their emergence and functionality remain unclear due to opaque pre-training processes. In this work, we investigate the formation of task vectors in a controlled setting, using models trained from scratch on synthetic datasets. Our findings confirm that task vectors naturally emerge under certain conditions, but the tasks may be relatively weakly and/or non-locally encoded within the model. To promote strong task vectors encoded at a prescribed location within the model, we propose an auxiliary training mechanism based on a task vector prompting loss (TVP-loss). This method eliminates the need to search for task-correlated encodings within the trained model and demonstrably improves robustness and generalization.

We propose a novel cooperative multi-agent reinforcement learning (MARL) approach for networked agents. In contrast to previous methods that rely on complete state information or joint observations, our agents must learn how to reach shared objectives under partial observability. During training, they collect individual rewards and approximate a team value function through local communication, resulting in cooperative behavior. To describe our problem, we introduce the networked dynamic partially observable Markov game framework, where agents communicate over a switching topology communication network. Our distributed method, DNA-MARL, uses a consensus mechanism for local communication and gradient descent for local computation. DNA-MARL increases the range of the possible applications of networked agents, being well-suited for real world domains that impose privacy and where the messages may not reach their recipients. We evaluate DNA-MARL across benchmark MARL scenarios. Our results highlight the superior performance of DNA-MARL over previous methods.

Generative AI systems like foundation models (FMs) must align well with human values to ensure their behavior is helpful and trustworthy. While Reinforcement Learning from Human Feedback (RLHF) has shown promise for optimizing model performance using human judgments, existing RLHF pipelines predominantly rely on immediate feedback, which can fail to accurately reflect the downstream impact of an interaction on users' utility. We demonstrate that feedback based on evaluators' foresight estimates of downstream consequences systematically induces Goodhart's Law dynamics, incentivizing misaligned behaviors like sycophancy and deception and ultimately degrading user outcomes. To alleviate this, we propose decoupling evaluation from prediction by refocusing RLHF on hindsight feedback. Our theoretical analysis reveals that conditioning evaluator feedback on downstream observations mitigates misalignment and improves expected human utility, even when these observations are simulated by the AI system itself. To leverage this insight in a practical alignment algorithm, we introduce Reinforcement Learning from Hindsight Simulation (RLHS), which first simulates plausible consequences and then elicits feedback to assess what behaviors were genuinely beneficial in hindsight. We apply RLHS to two widely-employed online and offline preference optimization methods -- Proximal Policy Optimization (PPO) and Direct Preference Optimization (DPO) -- and show empirically that misalignment is significantly reduced with both methods. Through an online human user study, we show that RLHS consistently outperforms RLHF in helping users achieve their goals and earns higher satisfaction ratings, despite being trained solely with simulated hindsight feedback. These results underscore the importance of focusing on long-term consequences, even simulated ones, to mitigate misalignment in RLHF.

Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one is commonly led to consider least fixpoints of (higher-dimensional) functions over the nonnegative reals. We show how to approximate the least fixpoint of such functions, focusing on the case in which they are not known precisely, but represented by a sequence of approximating functions that converge to them. We concentrate on monotone and non-expansive functions, for which uniqueness of fixpoints is not guaranteed and standard fixpoint iteration schemes might get stuck at a fixpoint that is not the least. Our main contribution is the identification of an iteration scheme, a variation of Mann iteration with a dampening factor, which, under suitable conditions, is shown to guarantee convergence to the least fixpoint of the function of interest. We then argue that these results are relevant in the context of model-based reinforcement learning for Markov decision processes (MDPs), showing that the proposed iteration scheme instantiates to MDPs and allows us to derive convergence to the optimal expected return. More generally, we show that our results can be used to iterate to the least fixpoint almost surely for systems where the function of interest can be approximated with given probabilistic error bounds, as it happens for probabilistic systems, such as simple stochastic games, that can be explored via sampling.

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an estimator observes n samples of a d -dimensional parameter vector \theta_{*}\in\mathbb{R} {d}, multiplied by a random sign S_i ( 1\le i\le n), and corrupted by isotropic standard Gaussian noise. As \delta varies, this model smoothly interpolates two well-studied models: the Gaussian Location Model for which \delta 0 and the Gaussian Mixture Model for which \delta 1/2 . We then provide an upper bound to the case of estimating \delta, assuming a (possibly inaccurate) knowledge of \theta_{*} . The bound is proved to be tight when \theta_{*} is an accurately known constant.

Bandits with knapsacks (BwK) is an influential model of sequential decision-making under uncertainty that incorporates resource consumption constraints. In each round, the decision-maker observes an outcome consisting of a reward and a vector of nonnegative resource consumptions, and the budget of each resource is decremented by its consumption. In this paper we introduce a natural generalization of the stochastic BwK problem that allows non-monotonic resource utilization. In each round, the decision-maker observes an outcome consisting of a reward and a vector of resource drifts that can be positive, negative or zero, and the budget of each resource is incremented by its drift. Our main result is a Markov decision process (MDP) policy that has constant regret against a linear programming (LP) relaxation when the decision-maker knows the true outcome distributions.

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model.