The paper addresses recovery of the observation sequence given known posterior state estimates, but unknown observations and/or sensor model and also in an extension, noise-corrupted measurements. There is a nice progression of the problem through IP, LP, and MILP followed by a more careful analytical derivation of the answers in the noise-free case, and a seemingly approximate though empirically effective approach (cf. Honestly, most of the motivations seem to be unrealistic, especially the cyber-physical security setting where one does not observe posteriors, but simply an action based on a presumed argmax w.r.t. The EEG application (while somewhat narrow) seems to be the best motivation, however, the sole example is to compare resconstructed observations to a redundant method of sensing -- is this really a compelling application? Is it actually used in practice?

The paper describes a sampling method for learning agent behaviors in interactive POMDPs (I-POMDPs). In general, I-POMDPs are a multi-agent POMDP model which, in addition to a belief about the environment state, the belief space includes nested recursive beliefs about the other agents' models. I-POMDP solutions, including the one proposed in the paper, largely approximate using a finite depth with either intentional models of others (e.g., their nested beliefs, state transitions, optimality criterion, etc.) or subintentional models of others (e.g., essentially "summaries of behavior" such as fictitious play). The proposed approach uses samples of the other agent at a particular depth to compute its values and policy. Related work on an interactive particle filter assumed the full frame was known (b, S, A, Omega, T, R, OC).

This paper addresses a potentially important problem by giving an algorithm that can solve large constrained POMDPs with online methods. A constrained POMDP, which augments a traditional POMDP with multi-attribute cost constraints, is an important extension that can help model a wider range of real-world phenomena than a POMDP can. Having such an algorithm for solving large CPOMDPs is a very valuable contribution. The authors provide, in this paper, a derivation of an unconstrained objective to be solved (resulting from taking the dual of the CPOMDP's linear program), backed by theoretical justification, and an adaptation of the online search algorithm, POMCP, that incorporates cost constraints by approximately optimizing the objective. The paper is extremely well-written, free of typos, and clear in its presentation.

This paper is very interesting. One previous assumption in TD learning is that reward are close with states in proximity of the state space, which has been pointed out by many papers is not realistic and have problems for spatial value function regularization. Instead, this paper make the assumption that rewards are close for states. Overall this paper has a very good motivation, and the literature review shows that the author is knowledgable of this field. This paper could open a novel area of temporal regularization that received inadequate attention before.

This is an excellent theoretical contribution. The analysis is quite heavy and has many subtleties. I do not have enough time to read the appended proofs; also, the subject of the paper is not in my area of research. The comments below are based on the impression I got after reading carefully the first 8 pages of the paper and glancing through the rest in the supplementary file. Summary: This paper is about reinforcement learning in weakly-communicating MDP under the average-reward criterion.

POST REBUTTAL: I do think that the edit to the proof suggested by the authors could work, but would lead to some exorbitant constant C4, a subject not addressed by the authors. Still, I have increased my score from "clear reject" to "accept" in the light of the fact that I am now happy with the validity of the proofs.

Large language models have demonstrated impressive in-context learning (ICL) capability. However, it is still unclear how the underlying transformers accomplish it, especially in more complex scenarios. Toward this goal, several recent works studied how transformers learn fixed-order Markov chains (FOMC) in context, yet natural languages are more suitably modeled by variable-order Markov chains (VOMC), i.e., context trees (CTs). In this work, we study the ICL of VOMC by viewing language modeling as a form of data compression and focus on small alphabets and low-order VOMCs. This perspective allows us to leverage mature compression algorithms, such as context-tree weighting (CTW) and prediction by partial matching (PPM) algorithms as baselines, the former of which is Bayesian optimal for a class of CTW priors. We empirically observe a few phenomena: 1) Transformers can indeed learn to compress VOMC in-context, while PPM suffers significantly; 2) The performance of transformers is not very sensitive to the number of layers, and even a two-layer transformer can learn in-context quite well; and 3) Transformers trained and tested on non-CTW priors can significantly outperform the CTW algorithm. To explain these phenomena, we analyze the attention map of the transformers and extract two mechanisms, on which we provide two transformer constructions: 1) A construction with $D+2$ layers that can mimic the CTW algorithm accurately for CTs of maximum order $D$, 2) A 2-layer transformer that utilizes the feed-forward network for probability blending. One distinction from the FOMC setting is that a counting mechanism appears to play an important role. We implement these synthetic transformer layers and show that such hybrid transformers can match the ICL performance of transformers, and more interestingly, some of them can perform even better despite the much-reduced parameter sets.

While large language models (LLMs) show impressive decision-making abilities, current methods lack a mechanism for automatic self-improvement from errors during task execution. We propose LEAP, an iterative fine-tuning framework that continually improves LLM agents using feedback from AI expert teachers. Our key insight is to equip the expert teachers with a privileged state -- information that is available during training but hidden at test time. This allows even weak experts to provide precise guidance, significantly improving the student agent's performance without access to privileged information at test time. We evaluate LEAP on diverse decision-making benchmarks, including text-based games (ALFWorld), web navigation (WebShop), and interactive coding (Intercode Bash). Our experiments show that LEAP (1) outperforms behavior cloning and ReAct baselines (2) enables weak student models (e.g., Llama3-8B) to exceed the performance of strong teacher models (GPT4-o), and (3) allows weak models to self-improve using privileged versions of themselves. We also provide a theoretical analysis showing that LEAP's success hinges on balancing privileged information with the student's realizability, which we empirically validate. Our code is available at https://leap-llm.github.io

Biological tree analysis serves as a pivotal tool in uncovering the evolutionary and differentiation relationships among organisms, genes, and cells. Its applications span diverse fields including phylogenetics, developmental biology, ecology, and medicine. Traditional tree inference methods, while foundational in early studies, face increasing limitations in processing the large-scale, complex datasets generated by modern high-throughput technologies. Recent advances in deep learning offer promising solutions, providing enhanced data processing and pattern recognition capabilities. However, challenges remain, particularly in accurately representing the inherently discrete and non-Euclidean nature of biological trees. In this review, we first outline the key biological priors fundamental to phylogenetic and differentiation tree analyses, facilitating a deeper interdisciplinary understanding between deep learning researchers and biologists. We then systematically examine the commonly used data formats and databases, serving as a comprehensive resource for model testing and development. We provide a critical analysis of traditional tree generation methods, exploring their underlying biological assumptions, technical characteristics, and limitations. Current developments in deep learning-based tree generation are reviewed, highlighting both recent advancements and existing challenges. Furthermore, we discuss the diverse applications of biological trees across various biological domains. Finally, we propose potential future directions and trends in leveraging deep learning for biological tree research, aiming to guide further exploration and innovation in this field.

Policy evaluation is an important instrument for the comparison of different algorithms in Reinforcement Learning (RL). Yet even a precise knowledge of the value function $V^{\pi}$ corresponding to a policy $\pi$ does not provide reliable information on how far is the policy $\pi$ from the optimal one. We present a novel model-free upper value iteration procedure $({\sf UVIP})$ that allows us to estimate the suboptimality gap $V^{\star}(x) - V^{\pi}(x)$ from above and to construct confidence intervals for $V^\star$. Our approach relies on upper bounds to the solution of the Bellman optimality equation via martingale approach. We provide theoretical guarantees for ${\sf UVIP}$ under general assumptions and illustrate its performance on a number of benchmark RL problems.