We study the split Conformal Prediction method when applied to Markovian data. We quantify the gap in terms of coverage induced by the correlations in the data (compared to exchangeable data). This gap strongly depends on the mixing properties of the underlying Markov chain, and we prove that it typically scales as $\sqrt{t_\mathrm{mix}\ln(n)/n}$ (where $t_\mathrm{mix}$ is the mixing time of the chain). We also derive upper bounds on the impact of the correlations on the size of the prediction set. Finally we present $K$-split CP, a method that consists in thinning the calibration dataset and that adapts to the mixing properties of the chain. Its coverage gap is reduced to $t_\mathrm{mix}/(n\ln(n))$ without really affecting the size of the prediction set. We finally test our algorithms on synthetic and real-world datasets.

Automatic spelling correction stands as a pivotal challenge within the ambit of natural language processing (NLP), demanding nuanced solutions. Traditional spelling correction techniques are typically only capable of detecting and correcting non-word errors, such as typos and misspellings. However, context-sensitive errors, also known as real-word errors, are more challenging to detect because they are valid words that are used incorrectly in a given context. The Persian language, characterized by its rich morphology and complex syntax, presents formidable challenges to automatic spelling correction systems. Furthermore, the limited availability of Persian language resources makes it difficult to train effective spelling correction models. This paper introduces a cutting-edge approach for precise and efficient real-word error correction in Persian text. Our methodology adopts a structured, multi-tiered approach, employing semantic analysis, feature selection, and advanced classifiers to enhance error detection and correction efficacy. The innovative architecture discovers and stores semantic similarities between words and phrases in Persian text. The classifiers accurately identify real-word errors, while the semantic ranking algorithm determines the most probable corrections for real-word errors, taking into account specific spelling correction and context properties such as context, semantic similarity, and edit-distance measures. Evaluations have demonstrated that our proposed method surpasses previous Persian real-word error correction models. Our method achieves an impressive F-measure of 96.6% in the detection phase and an accuracy of 99.1% in the correction phase. These results clearly indicate that our approach is a highly promising solution for automatic real-word error correction in Persian text.

We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms are suitable for underlying Markov decision processes (MDPs) having an arbitrary probabilistic reward mechanism, including continuous reward distributions with unbounded support being potentially heavy-tailed. For a plain instance of our proposed class of algorithms we prove error bounds, both within Wasserstein and Kolmogorov--Smirnov distances. Furthermore, for return distributions having probability density functions the algorithms yield approximations for these densities; error bounds are given within supremum norm. We introduce the concept of quantile-spline discretizations to come up with algorithms showing promising results in simulation experiments. While the performance of our algorithms can rigorously be analysed they can be seen as universal black box algorithms applicable to a large class of MDPs. We also derive new properties of probability metrics commonly used in DRL on which our quantitative analysis is based.

The importance of these seed stocks is underscored by the critical need for timely fulfillment of seed orders to meet specific planting windows, often mandated by the seasonal growth cycles of different crops. Failure to meet these strict timelines can lead to a host of downstream issues, including suboptimal crop yields and financial loss [1]. Figure 1: Overview of the centralized seed fulfillment process. The process begins with the arrival of seed stocks from multiple sites with stochastic, a priori unknown arrival distributions and ends with the fulfillment of orders with different deadlines and quantities. Our proposed adaptive adaptive hybrid tree search approach provides an efficient solution to the wave scheduling problem, optimizing the process of order fulfillment. Order fulfillment in industries such as e-commerce [2] and retail [3] often involve centralized fulfillment centers that simultaneously process arriving inventory and fulfill orders based on their deadlines. The fulfillment process with large catalogs often handle a batch of orders, hereinafter referred to as wave, together using automated sortation systems [4]. The supply chain in these sectors is typically well-established, with known inventory quantities and deterministic restock times. The problem of optimally scheduling waves to maximize fulfillment efficiency is addressed using traditional operations research and optimization techniques [5], [6] as order deadlines and inventory levels are known a priori or can be forecasted with low uncertainty.

Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally approximate. Recent work on using neural network models to reconstruct the mapping from the data space to the parameters from a set of synthetic parameter-data pairs suffers from the curse of dimensionality, resulting in inaccurate estimation as the data size grows. We propose a dimension-reduced approach to likelihood-free estimation which combines the ideas of reconstruction map estimation with dimension-reduction approaches based on subject-specific knowledge. We examine the properties of reconstruction map estimation with and without dimension reduction and explore the trade-off between approximation error due to information loss from reducing the data dimension and approximation error. Numerical examples show that the proposed approach compares favorably with reconstruction map estimation, approximate Bayesian computation, and synthetic likelihood estimation.

State of the art methods for target tracking with sensor management (or controlled sensing) are model-based and are obtained through solutions to Partially Observable Markov Decision Process (POMDP) formulations. In this paper a Reinforcement Learning (RL) approach to the problem is explored for the setting where the motion model for the object/target to be tracked is unknown to the observer. It is assumed that the target dynamics are stationary in time, the state space and the observation space are discrete, and there is complete observability of the location of the target under certain (a priori unknown) sensor control actions. Then, a novel Markov Decision Process (MDP) rather than POMDP formulation is proposed for the tracking problem with controlled sensing, which is termed as Track-MDP. In contrast to the POMDP formulation, the Track-MDP formulation is amenable to an RL based solution. It is shown that the optimal policy for the Track-MDP formulation, which is approximated through RL, is guaranteed to track all significant target paths with certainty. The Track-MDP method is then compared with the optimal POMDP policy, and it is shown that the infinite horizon tracking reward of the optimal Track-MDP policy is the same as that of the optimal POMDP policy. In simulations it is demonstrated that Track-MDP based RL leads to a policy that can track the target with high accuracy.

We present an optimistic Q-learning algorithm for regret minimization in average reward reinforcement learning under an additional assumption on the underlying MDP that for all policies, the expected time to visit some frequent state $s_0$ is finite and upper bounded by $H$. Our setting strictly generalizes the episodic setting and is significantly less restrictive than the assumption of bounded hitting time {\it for all states} made by most previous literature on model-free algorithms in average reward settings. We demonstrate a regret bound of $\tilde{O}(H^5 S\sqrt{AT})$, where $S$ and $A$ are the numbers of states and actions, and $T$ is the horizon. A key technical novelty of our work is to introduce an $\overline{L}$ operator defined as $\overline{L} v = \frac{1}{H} \sum_{h=1}^H L^h v$ where $L$ denotes the Bellman operator. We show that under the given assumption, the $\overline{L}$ operator has a strict contraction (in span) even in the average reward setting. Our algorithm design then uses ideas from episodic Q-learning to estimate and apply this operator iteratively. Therefore, we provide a unified view of regret minimization in episodic and non-episodic settings that may be of independent interest.

This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. While diffusion models are widely known to provide excellent generative modeling capability, practical applications in domains such as biology require generating samples that maximize some desired metric (e.g., translation efficiency in RNA, docking score in molecules, stability in protein). In these cases, the diffusion model can be optimized not only to generate realistic samples but also to explicitly maximize the measure of interest. Such methods are based on concepts from reinforcement learning (RL). We explain the application of various RL algorithms, including PPO, differentiable optimization, reward-weighted MLE, value-weighted sampling, and path consistency learning, tailored specifically for fine-tuning diffusion models. We aim to explore fundamental aspects such as the strengths and limitations of different RL-based fine-tuning algorithms across various scenarios, the benefits of RL-based fine-tuning compared to non-RL-based approaches, and the formal objectives of RL-based fine-tuning (target distributions). Additionally, we aim to examine their connections with related topics such as classifier guidance, Gflownets, flow-based diffusion models, path integral control theory, and sampling from unnormalized distributions such as MCMC. The code of this tutorial is available at https://github.com/masa-ue/RLfinetuning_Diffusion_Bioseq

How can a scientist use a Reinforcement Learning (RL) algorithm to design experiments over a dynamical system's state space? In the case of finite and Markovian systems, an area called Active Exploration (AE) relaxes the optimization problem of experiments design into Convex RL, a generalization of RL admitting a wider notion of reward. Unfortunately, this framework is currently not scalable and the potential of AE is hindered by the vastness of experiment spaces typical of scientific discovery applications. However, these spaces are often endowed with natural geometries, e.g., permutation invariance in molecular design, that an agent could leverage to improve the statistical and computational efficiency of AE. To achieve this, we bridge AE and MDP homomorphisms, which offer a way to exploit known geometric structures via abstraction. Towards this goal, we make two fundamental contributions: we extend MDP homomorphisms formalism to Convex RL, and we present, to the best of our knowledge, the first analysis that formally captures the benefit of abstraction via homomorphisms on sample efficiency. Ultimately, we propose the Geometric Active Exploration (GAE) algorithm, which we analyse theoretically and experimentally in environments motivated by problems in scientific discovery.

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment) have emerged as recently as the last decade, and have driven substantial recent practical and theoretical advances in the field. A particular focus is on methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI.