Peer prediction refers to a collection of mechanisms for eliciting information from human agents when direct verification of the obtained information is unavailable. They are designed to have a game-theoretic equilibrium where everyone reveals their private information truthfully. This result holds under the assumption that agents are Bayesian and they each adopt a fixed strategy across all tasks. Human agents however are observed in many domains to exhibit learning behavior in sequential settings. In this paper, we explore the dynamics of sequential peer prediction mechanisms when participants are learning agents.

We study the asynchronous stochastic gradient descent algorithm, for distributed training over n workers that might be heterogeneous. In this algorithm, workers compute stochastic gradients in parallel at their own pace and return them to the server without any synchronization.Existing convergence rates of this algorithm for non-convex smooth objectives depend on the maximum delay \tau_{\max} and reach an \epsilon -stationary point after O\!\left(\sigma 2\epsilon {-2} \tau_{\max}\epsilon {-1}\right) iterations, where \sigma is the variance of stochastic gradients. We also provide (ii) a simple delay-adaptive learning rate scheme, under which asynchronous SGD achieves a convergence rate of O\!\left(\sigma 2\epsilon {-2} \tau_{avg}\epsilon {-1}\right), and does not require any extra hyperparameter tuning nor extra communications. In addition, (iii) we consider the case of heterogeneous functions motivated by federated learning applications and improve the convergence rate by proving a weaker dependence on the maximum delay compared to prior works.

We aim for source-free domain adaptation, where the task is to deploy a model pre-trained on source domains to target domains. The challenges stem from the distribution shift from the source to the target domain, coupled with the unavailability of any source data and labeled target data for optimization. Rather than fine-tuning the model by updating the parameters, we propose to perturb the source model to achieve adaptation to target domains. We introduce perturbations into the model parameters by variational Bayesian inference in a probabilistic framework. By doing so, we can effectively adapt the model to the target domain while largely preserving the discriminative ability.

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few. Unrolled differentiation is a popular heuristic that approximates the solution using an iterative solver and differentiates it through the computational path. This work provides a non-asymptotic convergence-rate analysis of this approach on quadratic objectives for gradient descent and the Chebyshev method. We show that to ensure convergence of the Jacobian, we can either 1) choose a large learning rate leading to a fast asymptotic convergence but accept that the algorithm may have an arbitrarily long burn-in phase or 2) choose a smaller learning rate leading to an immediate but slower convergence. We refer to this phenomenon as the curse of unrolling.Finally, we discuss open problems relative to this approach, such as deriving a practical update rule for the optimal unrolling strategy and making novel connections with the field of Sobolev orthogonal polynomials.

We present Neural Shape Deformation Priors, a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements. State-of-the-art methods cast this problem as an optimization task, where the input source mesh is iteratively deformed to minimize an objective function according to hand-crafted regularizers such as ARAP. In this work, we learn the deformation behavior based on the underlying geometric properties of a shape, while leveraging a large-scale dataset containing a diverse set of non-rigid deformations. Specifically, given a source mesh and desired target locations of handles that describe the partial surface deformation, we predict a continuous deformation field that is defined in 3D space to describe the space deformation. To this end, we introduce transformer-based deformation networks that represent a shape deformation as a composition of local surface deformations. It learns a set of local latent codes anchored in 3D space, from which we can learn a set of continuous deformation functions for local surfaces.

In recent years, federated learning (FL) has emerged as an important distributed machine learning paradigm to collaboratively learn a global model with multiple clients, while keeping data local and private. However, a key assumption in most existing works on FL algorithms' convergence analysis is that the noise in stochastic first-order information has a finite variance. Although this assumption covers all light-tailed (i.e., sub-exponential) and some heavy-tailed noise distributions (e.g., log-normal, Weibull, and some Pareto distributions), it fails for many fat-tailed noise distributions (i.e., heavier-tailed'' with potentially infinite variance) that have been empirically observed in the FL literature. To date, it remains unclear whether one can design convergent algorithms for FL systems that experience fat-tailed noise. Specifically, for the largest \alpha \in (1,2] such that the fat-tailed noise in FL still has a bounded \alpha -moment, we show that both variants achieve \mathcal{O}((mT) {\frac{2-\alpha}{\alpha}}) and \mathcal{O}((mT) {\frac{1-\alpha}{3\alpha-2}}) convergence rates in the strongly-convex and general non-convex settings, respectively, where m and T are the numbers of clients and communication rounds.

By combining robust regression and prior information, we develop an effective robust regression method that can resist adaptive adversarial attacks. Due to the widespread existence of noise and data corruption, it is necessary to recover the true regression parameters when a certain proportion of the response variables have been corrupted. Methods to overcome this problem often involve robust least-squares regression. However, few methods achieve good performance when dealing with severe adaptive adversarial attacks. Based on the combination of prior information and robust regression via hard thresholding, this paper proposes an algorithm that improves the breakdown point when facing adaptive adversarial attacks. Furthermore, to improve the robustness and reduce the estimation error caused by the inclusion of a prior, the idea of Bayesian reweighting is used to construct a more robust algorithm.

In this paper, we study the problem of bandits with knapsacks (BwK) in a non-stationary environment. The BwK problem generalizes the multi-arm bandit (MAB) problem to model the resource consumption associated with playing each arm. At each time, the decision maker/player chooses to play an arm, and s/he will receive a reward and consume certain amount of resource from each of the multiple resource types. The objective is to maximize the cumulative reward over a finite horizon subject to some knapsack constraints on the resources. Existing works study the BwK problem under either a stochastic or adversarial environment.

Deep learning has achieved many breakthroughs in modern classification tasks. Numerous architectures have been proposed for different data structures but when it comes to the loss function, the cross-entropy loss is the predominant choice. Recently, several alternative losses have seen revived interests for deep classifiers. In particular, empirical evidence seems to promote square loss but a theoretical justification is still lacking. In this work, we contribute to the theoretical understanding of square loss in classification by systematically investigating how it performs for overparametrized neural networks in the neural tangent kernel (NTK) regime.

We show that, for any sufficiently small fixed \epsilon 0, when both players in a general-sum two-player (bimatrix) game employ optimistic mirror descent (OMD) with smooth regularization, learning rate \eta O(\epsilon 2) and T \Omega(poly(1/\epsilon)) repetitions, either the dynamics reach an \epsilon -approximate Nash equilibrium (NE), or the average correlated distribution of play is an \Omega(poly(\epsilon)) -strong coarse correlated equilibrium (CCE): any possible unilateral deviation does not only leave the player worse, but will decrease its utility by \Omega(poly(\epsilon)) . As an immediate consequence, when the iterates of OMD are bounded away from being Nash equilibria in a bimatrix game, we guarantee convergence to an \emph{exact} CCE after only O(1) iterations. Our results reveal that uncoupled no-regret learning algorithms can converge to CCE in general-sum games remarkably faster than to NE in, for example, zero-sum games. To establish this, we show that when OMD does not reach arbitrarily close to a NE, the (cumulative) regret of both players is not only negative, but decays linearly with time. Given that regret is the canonical measure of performance in online learning, our results suggest that cycling behavior of no-regret learning algorithms in games can be justified in terms of efficiency.