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The development of Policy Iteration (PI) has inspired many recent algorithms for Reinforcement Learning (RL), including several policy gradient methods, that gained both theoretical soundness and empirical success on a variety of tasks. The theory of PI is rich in the context of centralized learning, but its study is still in the infant stage under the federated setting. This paper explores the federated version of Approximate PI (API) and derives its error bound, taking into account the approximation error introduced by environment heterogeneity. We theoretically prove that a proper client selection scheme can reduce this error bound. Based on the theoretical result, we propose a client selection algorithm to alleviate the additional approximation error caused by environment heterogeneity. Experiment results show that the proposed algorithm outperforms other biased and unbiased client selection methods on the federated mountain car problem by effectively selecting clients with a lower level of heterogeneity from the population distribution.

Large language models (LLMs) have demonstrated remarkable language proficiency, but they face challenges when solving interactive tasks independently. Existing methods either rely on gradient access, which is often inaccessible in state-of-the-art LLMs like GPT-4, or necessitate diverse and high-quality in-context demonstrations. In this study, we propose LLM-PO, a novel approach that enables LLMs to address these tasks without gradient access or extensive demonstrations. The key idea is to maintain a text-based plan and ask LLMs to reflect on pros and cons of the current plan based on experience collected with it, to update the plan, and to collect more experiences with the new plan. Experiments on HotpotQA demonstrate that LLM-PO achieves higher or on par success rates compared to in-context learning (ICL) baselines while requiring less inference cost.

The remarkable advancements in large language models (LLMs) have significantly enhanced the performance in few-shot learning settings. By using only a small number of labeled examples, referred to as demonstrations, LLMs can effectively grasp the task at hand through in-context learning. However, the process of selecting appropriate demonstrations has received limited attention in prior work. This paper addresses the issue of identifying the most informative demonstrations for few-shot learning by approaching it as a pool-based Active Learning (AL) problem over a single iteration. Our objective is to investigate how AL algorithms can serve as effective demonstration selection methods for in-context learning. We compare various standard AL algorithms based on uncertainty, diversity, and similarity, and consistently observe that the latter outperforms all other methods, including random sampling. Notably, uncertainty sampling, despite its success in conventional supervised learning scenarios, performs poorly in this context. Our extensive experimentation involving a diverse range of GPT and OPT models across $24$ classification and multi-choice tasks, coupled with thorough analysis, unambiguously demonstrates that in-context example selection through AL prioritizes high-quality examples that exhibit low uncertainty and bear similarity to the test examples.

Overlapping instruction subsets derived from human originated code have previously been shown to dramatically shrink the inductive programming search space, often by many orders of magnitude. Here we extend the instruction subset approach to consider direct instruction-instruction applications (or instruction digrams) as an additional search heuristic for inductive programming. In this study we analyse the frequency distribution of instruction digrams in a large sample of open source code. This indicates that the instruction digram distribution is highly skewed with over 93% of possible instruction digrams not represnted in the code sample. We demonstrate that instruction digrams can be used to constrain instruction selection during search, further reducing size of the the search space, in some cases by several orders of magnitude. This significantly increases the size of programs that can be generated using search based inductive programming techniques. We discuss the results and provide some suggestions for further work.

Large language models (LLMs) have exhibited an emergent in-context learning (ICL) ability. However, the ICL models that can solve ordinary cases are hardly extended to solve more complex tasks by processing the demonstration examples once. This single-turn ICL is incoordinate with the decision making process of humans by learning from analogy. In this paper, we propose an effective and efficient two-stage framework to boost ICL in LLMs by exploiting a dual form between Transformer attention and gradient descent-based optimization. Concretely, we divide the ICL process into "Deep-Thinking" and inference stages. The "Deep-Thinking" stage performs iterative forward optimization of demonstrations, which is expected to boost the reasoning abilities of LLMs at test time by "thinking" demonstrations multiple times. It produces accumulated meta-gradients by manipulating the Key-Value matrices in the self-attention modules of the Transformer. Then, the inference stage only takes the test query as input without concatenating demonstrations and applies the learned meta-gradients through attention for output prediction. In this way, demonstrations are not required during the inference stage since they are already learned and stored in the definitive meta-gradients. LLMs can be effectively and efficiently adapted to downstream tasks. Extensive experiments on ten classification and multiple-choice datasets show that our method achieves substantially better performance than standard ICL in terms of both accuracy and efficiency.

The study of robustness has received much attention due to its inevitability in data-driven settings where many systems face uncertainty. One such example of concern is Bayesian Optimization (BO), where uncertainty is multi-faceted, yet there only exists a limited number of works dedicated to this direction. In particular, there is the work of Kirschner et al. (2020), which bridges the existing literature of Distributionally Robust Optimization (DRO) by casting the BO problem from the lens of DRO. While this work is pioneering, it admittedly suffers from various practical shortcomings such as finite contexts assumptions, leaving behind the main question Can one devise a computationally tractable algorithm for solving this DRO-BO problem? In this work, we tackle this question to a large degree of generality by considering robustness against data-shift in $\phi$-divergences, which subsumes many popular choices, such as the $\chi^2$-divergence, Total Variation, and the extant Kullback-Leibler (KL) divergence. We show that the DRO-BO problem in this setting is equivalent to a finite-dimensional optimization problem which, even in the continuous context setting, can be easily implemented with provable sublinear regret bounds. We then show experimentally that our method surpasses existing methods, attesting to the theoretical results.

Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.

Meta-learning extracts the common knowledge acquired from learning different tasks and uses it for unseen tasks. It demonstrates a clear advantage on tasks that have insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related via the shared model or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve the performance of few-shot learning. This type of graph is usually free or cheap to obtain but has rarely been explored in previous works. We study the prototype based few-shot classification, in which a prototype is generated for each class, such that the nearest neighbor search between the prototypes produces an accurate classification. We introduce "Gated Propagation Network (GPN)", which learns to propagate messages between prototypes of different classes on the graph, so that learning the prototype of each class benefits from the data of other related classes. In GPN, an attention mechanism is used for the aggregation of messages from neighboring classes, and a gate is deployed to choose between the aggregated messages and the message from the class itself. GPN is trained on a sequence of tasks from many-shot to few-shot generated by subgraph sampling. During training, it is able to reuse and update previously achieved prototypes from the memory in a life-long learning cycle. In experiments, we change the training-test discrepancy and test task generation settings for thorough evaluations. GPN outperforms recent meta-learning methods on two benchmark datasets in all studied cases.