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This work establishes the first framework of federated $\mathcal{X}$-armed bandit, where different clients face heterogeneous local objective functions defined on the same domain and are required to collaboratively figure out the global optimum. We propose the first federated algorithm for such problems, named \texttt{Fed-PNE}. By utilizing the topological structure of the global objective inside the hierarchical partitioning and the weak smoothness property, our algorithm achieves sublinear cumulative regret with respect to both the number of clients and the evaluation budget. Meanwhile, it only requires logarithmic communications between the central server and clients, protecting the client privacy. Experimental results on synthetic functions and real datasets validate the advantages of \texttt{Fed-PNE} over various centralized and federated baseline algorithms.

This paper considers the problem of distributed multi-agent learning, where the global aim is to minimize a sum of local objective (empirical loss) functions through local optimization and information exchange between neighbouring nodes. We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, which is based on GIANT, a Federated learning algorithm that relies on a centralized parameter server. The Network-GIANT algorithm is designed via a combination of gradient-tracking and a Newton-type iterative algorithm at each node with consensus based averaging of local gradient and Newton updates. We prove that our algorithm guarantees semi-global and exponential convergence to the exact solution over the network assuming strongly convex and smooth loss functions. We provide empirical evidence of the superior convergence performance of Network-GIANT over other state-of-art distributed learning algorithms such as Network-DANE and Newton-Raphson Consensus.

Distributed tensor decomposition (DTD) is a fundamental data-analytics technique that extracts latent important properties from high-dimensional multi-attribute datasets distributed over edge devices. Conventionally its wireless implementation follows a one-shot approach that first computes local results at devices using local data and then aggregates them to a server with communication-efficient techniques such as over-the-air computation (AirComp) for global computation. Such implementation is confronted with the issues of limited storage-and-computation capacities and link interruption, which motivates us to propose a framework of on-the-fly communication-and-computing (FlyCom$^2$) in this work. The proposed framework enables streaming computation with low complexity by leveraging a random sketching technique and achieves progressive global aggregation through the integration of progressive uploading and multiple-input-multiple-output (MIMO) AirComp. To develop FlyCom$^2$, an on-the-fly sub-space estimator is designed to take real-time sketches accumulated at the server to generate online estimates for the decomposition. Its performance is evaluated by deriving both deterministic and probabilistic error bounds using the perturbation theory and concentration of measure. Both results reveal that the decomposition error is inversely proportional to the population of sketching observations received by the server. To further rein in the noise effect on the error, we propose a threshold-based scheme to select a subset of sufficiently reliable received sketches for DTD at the server. Experimental results validate the performance gain of the proposed selection algorithm and show that compared to its one-shot counterparts, the proposed FlyCom$^2$ achieves comparable (even better in the case of large eigen-gaps) decomposition accuracy besides dramatically reducing devices' complexity costs.

Autonomous racing control is a challenging research problem as vehicles are pushed to their limits of handling to achieve an optimal lap time; therefore, vehicles exhibit highly nonlinear and complex dynamics. Difficult-to-model effects, such as drifting, aerodynamics, chassis weight transfer, and suspension can lead to infeasible and suboptimal trajectories. While offline planning allows optimizing a full reference trajectory for the minimum lap time objective, such modeling discrepancies are particularly detrimental when using offline planning, as planning model errors compound with controller modeling errors. Gaussian Process Regression (GPR) can compensate for modeling errors. However, previous works primarily focus on modeling error in real-time control without consideration for how the model used in offline planning can affect the overall performance. In this work, we propose a double-GPR error compensation algorithm to reduce model uncertainties; specifically, we compensate both the planner's model and controller's model with two respective GPR-based error compensation functions. Furthermore, we design an iterative framework to re-collect error-rich data using the racing control system. We test our method in the high-fidelity racing simulator Gran Turismo Sport (GTS); we find that our iterative, double-GPR compensation functions improve racing performance and iteration stability in comparison to a single compensation function applied merely for real-time control.

Communication compression is an essential strategy for alleviating communication overhead by reducing the volume of information exchanged between computing nodes in large-scale distributed stochastic optimization. Although numerous algorithms with convergence guarantees have been obtained, the optimal performance limit under communication compression remains unclear. In this paper, we investigate the performance limit of distributed stochastic optimization algorithms employing communication compression. We focus on two main types of compressors, unbiased and contractive, and address the best-possible convergence rates one can obtain with these compressors. We establish the lower bounds for the convergence rates of distributed stochastic optimization in six different settings, combining strongly-convex, generally-convex, or non-convex functions with unbiased or contractive compressor types. To bridge the gap between lower bounds and existing algorithms' rates, we propose NEOLITHIC, a nearly optimal algorithm with compression that achieves the established lower bounds up to logarithmic factors under mild conditions. Extensive experimental results support our theoretical findings. This work provides insights into the theoretical limitations of existing compressors and motivates further research into fundamentally new compressor properties.

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work we aim to approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error by evaluating it at the new solution. This treatment convexifies the problem and allows us to benefit from established convex optimization methods. We separately consider cases where the approximation is fixed over iterations and where the approximation is adaptive. In the fixed case we show theoretically under what assumptions the sequence converges. In the adaptive case, particularly considering the special case of approximation by first-order Taylor expansion, we show that with certain assumptions the sequence converges to a critical point of the original nonconvex functional. Furthermore, we show that with quadratic objective functions the sequence corresponds to the Gauss-Newton method. Finally, we showcase numerical results superior to the conventional model correction method. We also show, that a fixed approximation can provide competitive results with considerable computational speed-up.

This paper introduces Distribution-Flexible Subset Quantization (DFSQ), a post-training quantization method for super-resolution networks. Our motivation for developing DFSQ is based on the distinctive activation distributions of current super-resolution models, which exhibit significant variance across samples and channels. To address this issue, DFSQ conducts channel-wise normalization of the activations and applies distribution-flexible subset quantization (SQ), wherein the quantization points are selected from a universal set consisting of multi-word additive log-scale values. To expedite the selection of quantization points in SQ, we propose a fast quantization points selection strategy that uses K-means clustering to select the quantization points closest to the centroids. Compared to the common iterative exhaustive search algorithm, our strategy avoids the enumeration of all possible combinations in the universal set, reducing the time complexity from exponential to linear. Consequently, the constraint of time costs on the size of the universal set is greatly relaxed. Extensive evaluations of various super-resolution models show that DFSQ effectively retains performance even without fine-tuning. For example, when quantizing EDSRx2 on the Urban benchmark, DFSQ achieves comparable performance to full-precision counterparts on 6- and 8-bit quantization, and incurs only a 0.1 dB PSNR drop on 4-bit quantization. Code is at \url{//github.com/zysxmu/DFSQ}

Oracle networks feeding off-chain information to a blockchain are required to solve a distributed agreement problem since these networks receive information from multiple sources and at different times. We make a key observation that in most cases, the value obtained by oracle network nodes from multiple information sources are in close proximity. We define a notion of agreement distance and leverage the availability of a state machine replication (SMR) service to solve this distributed agreement problem with an honest simple majority of nodes instead of the conventional requirement of an honest super majority of nodes. Values from multiple nodes being in close proximity, therefore, forming a coherent cluster, is one of the keys to its efficiency. Our asynchronous protocol also embeds a fallback mechanism if the coherent cluster formation fails. Through simulations using real-world exchange data from seven prominent exchanges, we show that even for very small agreement distance values, the protocol would be able to form coherent clusters and therefore, can safely tolerate up to $1/2$ fraction of Byzantine nodes. We also show that, for a small statistical error, it is possible to choose the size of the oracle network to be significantly smaller than the entire system tolerating up to a $1/3$ fraction of Byzantine failures. This allows the oracle network to operate much more efficiently and horizontally scale much better.

In this paper, we put forward the model of zero-error distributed function compression system of two binary memoryless sources X and Y, where there are two encoders En1 and En2 and one decoder De, connected by two channels (En1, De) and (En2, De) with the capacity constraints C1 and C2, respectively. The encoder En1 can observe X or (X,Y) and the encoder En2 can observe Y or (X,Y) according to the two switches s1 and s2 open or closed (corresponding to taking values 0 or 1). The decoder De is required to compress the binary arithmetic sum f(X,Y)=X+Y with zero error by using the system multiple times. We use (s1s2;C1,C2;f) to denote the model in which it is assumed that C1 \geq C2 by symmetry. The compression capacity for the model is defined as the maximum average number of times that the function f can be compressed with zero error for one use of the system, which measures the efficiency of using the system. We fully characterize the compression capacities for all the four cases of the model (s1s2;C1,C2;f) for s1s2= 00,01,10,11. Here, the characterization of the compression capacity for the case (01;C1,C2;f) with C1>C2 is highly nontrivial, where a novel graph coloring approach is developed. Furthermore, we apply the compression capacity for (01;C1,C2;f) to an open problem in network function computation that whether the best known upper bound of Guang et al. on computing capacity is in general tight.

Recent work has shown that standard training via empirical risk minimization (ERM) can produce models that achieve high accuracy on average but low accuracy on underrepresented groups due to the prevalence of spurious features. A predominant approach to tackle this group robustness problem minimizes the worst group error (akin to a minimax strategy) on the training data, hoping it will generalize well on the testing data. However, this is often suboptimal, especially when the out-of-distribution (OOD) test data contains previously unseen groups. Inspired by ideas from the information retrieval and learning-to-rank literature, this paper first proposes to use Discounted Cumulative Gain (DCG) as a metric of model quality for facilitating better hyperparameter tuning and model selection. Being a ranking-based metric, DCG weights multiple poorly-performing groups (instead of considering just the group with the worst performance). As a natural next step, we build on our results to propose a ranking-based training method called Discounted Rank Upweighting (DRU), which differentially reweights a ranked list of poorly-performing groups in the training data to learn models that exhibit strong OOD performance on the test data. Results on several synthetic and real-world datasets highlight the superior generalization ability of our group-ranking-based (akin to soft-minimax) approach in selecting and learning models that are robust to group distributional shifts.