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Switching costs, which capture the costs for changing policies, are regarded as a critical metric in reinforcement learning (RL), in addition to the standard metric of losses (or rewards). However, existing studies on switching costs (with a coefficient $\beta$ that is strictly positive and is independent of $T$) have mainly focused on static RL, where the loss distribution is assumed to be fixed during the learning process, and thus practical scenarios where the loss distribution could be non-stationary or even adversarial are not considered. While adversarial RL better models this type of practical scenarios, an open problem remains: how to develop a provably efficient algorithm for adversarial RL with switching costs? This paper makes the first effort towards solving this problem. First, we provide a regret lower-bound that shows that the regret of any algorithm must be larger than $\tilde{\Omega}( ( H S A )^{1/3} T^{2/3} )$, where $T$, $S$, $A$ and $H$ are the number of episodes, states, actions and layers in each episode, respectively. Our lower bound indicates that, due to the fundamental challenge of switching costs in adversarial RL, the best achieved regret (whose dependency on $T$ is $\tilde{O}(\sqrt{T})$) in static RL with switching costs (as well as adversarial RL without switching costs) is no longer achievable. Moreover, we propose two novel switching-reduced algorithms with regrets that match our lower bound when the transition function is known, and match our lower bound within a small factor of $\tilde{O}( H^{1/3} )$ when the transition function is unknown. Our regret analysis demonstrates the near-optimal performance of them.

The complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC'14). There are two complexity classes that can be considered quantum analogues of classical free games: (1) AM*, the multiprover interactive proof class corresponding to free games with entangled players, and, somewhat less obviously, (2) BellQMA(2), the class of quantum Merlin-Arthur proof systems with two unentangled Merlins, whose proof states are separately measured by Arthur. In this work, we make significant progress towards a tight characterization of both of these classes. 1. We show a BellQMA(2) protocol for 3SAT on $n$ variables, where the total amount of communication is $\tilde{O}(\sqrt{n})$. This answers an open question of Chen and Drucker (2010) and also shows, conditional on ETH, that the algorithm of Brand\~{a}o, Christandl and Yard (STOC'11) is tight up to logarithmic factors. 2. We show that $\mathsf{AM}^*[n_{\text{provers}} = 2, q = O(1), a =\mathrm{poly}\log(n)] = \mathsf{RE}$, i.e. that free entangled games with constant-sized questions are as powerful as general entangled games. Our result is a significant improvement over the headline result of Ji et al. (2020), whose MIP* protocol for the halting problem has $\mathrm{poly}(n)$-sized questions and answers. 3. We obtain a zero-gap AM* protocol for a $\Pi_2$ complete language with constant-size questions and almost logarithmically large answers, improving on the headline result of Mousavi, Nezhadi and Yuen (STOC'22). 4. Using a connection to the nonuniform complexity of the halting problem we show that any MIP* protocol for RE requires $\Omega(\log n)$ bits of communication. It follows that our results in item 3 are optimal up to an $O(\log^* n)$ factor, and that the gapless compression theorems of MNY'22 are asymptotically optimal.

Offline reinforcement learning (RL) aims to find an optimal policy for sequential decision-making using a pre-collected dataset, without further interaction with the environment. Recent theoretical progress has focused on developing sample-efficient offline RL algorithms with various relaxed assumptions on data coverage and function approximators, especially to handle the case with excessively large state-action spaces. Among them, the framework based on the linear-programming (LP) reformulation of Markov decision processes has shown promise: it enables sample-efficient offline RL with function approximation, under only partial data coverage and realizability assumptions on the function classes, with favorable computational tractability. In this work, we revisit the LP framework for offline RL, and provide a new reformulation that advances the existing results in several aspects, relaxing certain assumptions and achieving optimal statistical rates in terms of sample size. Our key enabler is to introduce proper constraints in the reformulation, instead of using any regularization as in the literature, also with careful choices of the function classes and initial state distributions. We hope our insights bring into light the use of LP formulations and the induced primal-dual minimax optimization, in offline RL.

As the availability of omics data has increased in the last few years, more multi-omics data have been generated, that is, high-dimensional molecular data consisting of several types such as genomic, transcriptomic, or proteomic data, all obtained from the same patients. Such data lend themselves to being used as covariates in automatic outcome prediction because each omics type may contribute unique information, possibly improving predictions compared to using only one omics data type. Frequently, however, in the training data and the data to which automatic prediction rules should be applied, the test data, the different omics data types are not available for all patients. We refer to this type of data as block-wise missing multi-omics data. First, we provide a literature review on existing prediction methods applicable to such data. Subsequently, using a collection of 13 publicly available multi-omics data sets, we compare the predictive performances of several of these approaches for different block-wise missingness patterns. Finally, we discuss the results of this empirical comparison study and draw some tentative conclusions.

Federated learning (FL) has been proposed to protect data privacy and virtually assemble the isolated data silos by cooperatively training models among organizations without breaching privacy and security. However, FL faces heterogeneity from various aspects, including data space, statistical, and system heterogeneity. For example, collaborative organizations without conflict of interest often come from different areas and have heterogeneous data from different feature spaces. Participants may also want to train heterogeneous personalized local models due to non-IID and imbalanced data distribution and various resource-constrained devices. Therefore, heterogeneous FL is proposed to address the problem of heterogeneity in FL. In this survey, we comprehensively investigate the domain of heterogeneous FL in terms of data space, statistical, system, and model heterogeneity. We first give an overview of FL, including its definition and categorization. Then, We propose a precise taxonomy of heterogeneous FL settings for each type of heterogeneity according to the problem setting and learning objective. We also investigate the transfer learning methodologies to tackle the heterogeneity in FL. We further present the applications of heterogeneous FL. Finally, we highlight the challenges and opportunities and envision promising future research directions toward new framework design and trustworthy approaches.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.