We study the problem of augmenting online algorithms with machine learned (ML) advice. In particular, we consider the multi-shop ski rental (MSSR) problem, which is a generalization of the classical ski rental problem. In MSSR, each shop has different prices for buying and renting a pair of skis, and a skier has to make decisions on when and where to buy. We obtain both deterministic and randomized online algorithms with provably improved performance when either a single or multiple ML predictions are used to make decisions. These online algorithms have no knowledge about the quality or the prediction error type of the ML prediction. The performance of these online algorithms are robust to the poor performance of the predictors, but improve with better predictions. Extensive experiments using both synthetic and real world data traces verify our theoretical observations and show better performance against algorithms that purely rely on online decision making.

We consider the problem of controlling an unknown stochastic linear system with quadratic costs - called the adaptive LQ control problem. We re-examine an approach called "Reward-Biased Maximum Likelihood Estimate" (RBMLE) [1] that was proposed more than forty years ago, and which predates the "Upper Confidence Bound" (UCB) method as well as the definition of "regret" for bandit problems [2]. It simply added a term favoring parameters with larger rewards to the criterion for parameter estimation. We show how the RBMLE and UCB methods can be reconciled, and thereby propose an Augmented RBMLE-UCB algorithm that combines the penalty of the RBMLE method with the constraints of the UCB method [3], uniting the two approaches to optimism in the face of uncertainty. We establish that theoretically, this method retains Õ( T) regret, the best known so far. We further compare the empirical performance of the proposed Augmented RBMLE-UCB and the standard RBMLE (without the augmentation) with UCB, Thompson Sampling, Input Perturbation, Randomized Certainty Equivalence and StabL on many real-world examples including flight control of Boeing 747 and Unmanned Aerial Vehicle. We perform extensive simulation studies showing that the Augmented RBMLE consistently outperforms UCB, Thompson Sampling and StabL by a huge margin, while it is marginally better than Input Perturbation and moderately better than Randomized Certainty Equivalence.

Its value also depends on the bitwidth of the machine as well as the dimension of the dataset. In particular, in order to speed up the running time of matrix-matrix multiplication, we do a modular operation after the inner product of vectors instead of doing a modular operation per product of each element. A.2 Proof of Theorem 1 First, we show that the minimum number of clients needed for our decoding operation to be successful, i.e., the recovery threshold of COPML, is equal to (2r +1)(K +T 1)+1. To do so, we demonstrate in the following that the decoding process will be successful as long as N (2r +1)(K +T 1)+1. As described in Section 3, given the polynomial approximation of the sigmoid function in (5), the degree of h(z) in (8) is at most (2r + 1)(K + T 1).

We consider a collaborative learning scenario in which multiple data-owners wish to jointly train a logistic regression model, while keeping their individual datasets private from the other parties. We propose COPML, a fully-decentralized training framework that achieves scalability and privacy-protection simultaneously. The key idea of COPML is to securely encode the individual datasets to distribute the computation load effectively across many parties and to perform the training computations as well as the model updates in a distributed manner on the securely encoded data. We provide the privacy analysis of COPML and prove its convergence. Furthermore, we experimentally demonstrate that COPML can achieve significant speedup in training over the benchmark protocols. Our protocol provides strong statistical privacy guarantees against colluding parties (adversaries) with unbounded computational power, while achieving up to 16 speedup in the training time against the benchmark protocols.

We introduce a dynamic benchmarking system for conversational agents that evaluates their performance through a single, simulated, and lengthy user agent interaction. The interaction is a conversation between the user and agent, where multiple tasks are introduced and then undertaken concurrently. We context switch regularly to interleave the tasks, which constructs a realistic testing scenario in which we assess the Long-Term Memory, Continual Learning, and Information Integration capabilities of the agents. Results from both proprietary and open-source Large-Language Models show that LLMs in general perform well on single-task interactions, but they struggle on the same tasks when they are interleaved. Notably, short-context LLMs supplemented with an LTM system perform as well as or better than those with larger contexts. Our benchmark suggests that there are other challenges for LLMs responding to more natural interactions that contemporary benchmarks have heretofore not been able to capture.

Neural networks (NN) are extensively studied in cutting-edge soft sensor models due to their feature extraction and function approximation capabilities. Current research into network-based methods primarily focuses on models' offline accuracy. Notably, in industrial soft sensor context, online optimizing stability and interpretability are prioritized, followed by accuracy. This requires a clearer understanding of network's training process. To bridge this gap, we propose a novel NN named the Approximated Orthogonal Projection Unit (AOPU) which has solid mathematical basis and presents superior training stability. AOPU truncates the gradient backpropagation at dual parameters, optimizes the trackable parameters updates, and enhances the robustness of training. We further prove that AOPU attains minimum variance estimation (MVE) in NN, wherein the truncated gradient approximates the natural gradient (NG). Empirical results on two chemical process datasets clearly show that AOPU outperforms other models in achieving stable convergence, marking a significant advancement in soft sensor field.

Orthogonal Monte Carlo [43] (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods [18] to predictive recurrent neural networks [11], generative models [36] and reinforcement learning [16]. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. As a corollary, we manage to obtain first uniform convergence results for OMCs and consequently, substantially strengthen best known downstream guarantees for kernel ridge regression via OMCs. We also propose novel extensions of the method leveraging theory of algebraic varieties over finite fields and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.

Transformer models excel at capturing long-range dependencies in sequential data, but lack explicit mechanisms to leverage structural patterns inherent in fixed-length input sequences. In this paper, we propose a novel sequence structure learning and modulation approach that endows Transformers with the ability to model and utilize such fixed-sequence structural properties for improved performance on inertial pose estimation tasks. Specifically, our method introduces a Sequence Structure Module (SSM) that utilizes structural information of fixed-length inertial sensor readings to adjust the input features of transformers. Such structural information can either be acquired by learning or specified based on users' prior knowledge. To justify the prospect of our approach, we show that i) injecting spatial structural information of IMUs/joints learned from data improves accuracy, while ii) injecting temporal structural information based on smooth priors reduces jitter (i.e., improves steadiness), in a spatial-temporal transformer solution for inertial pose estimation. Extensive experiments across multiple benchmark datasets demonstrate the superiority of our approach against state-of-the-art methods and has the potential to advance the design of the transformer architecture for fixed-length sequences.

In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution, and each arm can be sampled further to obtain noisy estimates of the average reward of that arm. Prior work focuses on identifying the best arm, i.e., estimating the maximum of the average reward distribution. We consider a general class of distribution functionals beyond the maximum, and propose unified meta algorithms for both the offline and online settings, achieving optimal sample complexities. We show that online estimation, where the learner can sequentially choose whether to sample a new or existing arm, offers no advantage over the offline setting for estimating the mean functional, but significantly reduces the sample complexity for other functionals such as the median, maximum, and trimmed mean. The matching lower bounds utilize several different Wasserstein distances. For the special case of median estimation, we identify a curious thresholding phenomenon on the indistinguishability between Gaussian convolutions with respect to the noise level, which may be of independent interest.

In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution, and each arm can be sampled further to obtain noisy estimates of the average reward of that arm. Prior work focuses on identifying the best arm, i.e., estimating the maximum of the average reward distribution. We consider a general class of distribution functionals beyond the maximum, and propose unified meta algorithms for both the offline and online settings, achieving optimal sample complexities. We show that online estimation, where the learner can sequentially choose whether to sample a new or existing arm, offers no advantage over the offline setting for estimating the mean functional, but significantly reduces the sample complexity for other functionals such as the median, maximum, and trimmed mean. The matching lower bounds utilize several different Wasserstein distances. For the special case of median estimation, we identify a curious thresholding phenomenon on the indistinguishability between Gaussian convolutions with respect to the noise level, which may be of independent interest.