Pre-trained multilingual speech foundation models, like Whisper, have shown impressive performance across different languages. However, adapting these models to new or specific languages is computationally extensive and faces catastrophic forgetting problems. Addressing these issues, our study investigates strategies to enhance the model on new languages in the absence of original training data, while also preserving the established performance on the original languages. Specifically, we first compare various LoRA-based methods to find out their vulnerability to forgetting. To mitigate this issue, we propose to leverage the LoRA parameters from the original model for approximate orthogonal gradient descent on the new samples. Additionally, we also introduce a learnable rank coefficient to allocate trainable parameters for more efficient training. Our experiments with a Chinese Whisper model (for Uyghur and Tibetan) yield better results with a more compact parameter set.

Differentially private stochastic gradient descent (DP-SGD) has been instrumental in privately training deep learning models by providing a framework to control and track the privacy loss incurred during training. At the core of this computation lies a subsampling method that uses a privacy amplification lemma to enhance the privacy guarantees provided by the additive noise. Fixed size subsampling is appealing for its constant memory usage, unlike the variable sized minibatches in Poisson subsampling. It is also of interest in addressing class imbalance and federated learning. However, the current computable guarantees for fixed-size subsampling are not tight and do not consider both add/remove and replace-one adjacency relationships. We present a new and holistic R{\'e}nyi differential privacy (RDP) accountant for DP-SGD with fixed-size subsampling without replacement (FSwoR) and with replacement (FSwR). For FSwoR we consider both add/remove and replace-one adjacency. Our FSwoR results improves on the best current computable bound by a factor of $4$. We also show for the first time that the widely-used Poisson subsampling and FSwoR with replace-one adjacency have the same privacy to leading order in the sampling probability. Accordingly, our work suggests that FSwoR is often preferable to Poisson subsampling due to constant memory usage. Our FSwR accountant includes explicit non-asymptotic upper and lower bounds and, to the authors' knowledge, is the first such analysis of fixed-size RDP with replacement for DP-SGD. We analytically and empirically compare fixed size and Poisson subsampling, and show that DP-SGD gradients in a fixed-size subsampling regime exhibit lower variance in practice in addition to memory usage benefits.

We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing deterministic policy gradient methods in continuous state and action spaces is particularly challenging due to the lack of enumerable state-action pairs and the adoption of deterministic policies, hindering the application of existing policy gradient methods for constrained MDPs. To this end, we develop a deterministic policy gradient primal-dual method to find an optimal deterministic policy with non-asymptotic convergence. Specifically, we leverage regularization of the Lagrangian of the constrained MDP to propose a deterministic policy gradient primal-dual (D-PGPD) algorithm that updates the deterministic policy via a quadratic-regularized gradient ascent step and the dual variable via a quadratic-regularized gradient descent step. We prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair. We instantiate D-PGPD with function approximation and prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair, up to a function approximation error. Furthermore, we demonstrate the effectiveness of our method in two continuous control problems: robot navigation and fluid control. To the best of our knowledge, this appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.

Bayesian Neural Networks(BNNs) with high-dimensional parameters pose a challenge for posterior inference due to the multi-modality of the posterior distributions. Stochastic Gradient MCMC(SGMCMC) with cyclical learning rate scheduling is a promising solution, but it requires a large number of sampling steps to explore high-dimensional multi-modal posteriors, making it computationally expensive. In this paper, we propose a meta-learning strategy to build \gls{sgmcmc} which can efficiently explore the multi-modal target distributions. Our algorithm allows the learned SGMCMC to quickly explore the high-density region of the posterior landscape. Also, we show that this exploration property is transferrable to various tasks, even for the ones unseen during a meta-training stage. Using popular image classification benchmarks and a variety of downstream tasks, we demonstrate that our method significantly improves the sampling efficiency, achieving better performance than vanilla \gls{sgmcmc} without incurring significant computational overhead.

Mean field games (MFGs) model the interactions within a large-population multi-agent system using the population distribution. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), which calculates best responses and induced population distribution separately and sequentially. However, FPI-type methods suffer from inefficiency and instability, due to oscillations caused by the forward-backward procedure. This paper considers an online learning method for MFGs, where an agent updates its policy and population estimates simultaneously and fully asynchronously, resulting in a simple stochastic gradient descent (SGD) type method called SemiSGD. Not only does SemiSGD exhibit numerical stability and efficiency, but it also provides a novel perspective by treating the value function and population distribution as a unified parameter. We theoretically show that SemiSGD directs this unified parameter along a descent direction to the mean field equilibrium. Motivated by this perspective, we develop a linear function approximation (LFA) for both the value function and the population distribution, resulting in the first population-aware LFA for MFGs on continuous state-action space. Finite-time convergence and approximation error analysis are provided for SemiSGD equipped with population-aware LFA.

Many important managerial decisions are made based on censored observations. Making decisions without adequately handling the censoring leads to inferior outcomes. We investigate the data-driven decision-making problem with an offline dataset containing the feature data and the censored historical data of the variable of interest without the censoring indicators. Without assuming the underlying distribution, we design and leverage {\epsilon}-insensitive operational costs to deal with the unobserved censoring in an offline data-driven fashion. We demonstrate the customization of the {\epsilon}-insensitive operational costs for a newsvendor problem and use such costs to train two representative ML models, including linear regression (LR) models and neural networks (NNs). We derive tight generalization bounds for the custom LR model without regularization (LR-{\epsilon}NVC) and with regularization (LR-{\epsilon}NVC-R), and a high-probability generalization bound for the custom NN (NN-{\epsilon}NVC) trained by stochastic gradient descent. The theoretical results reveal the stability and learnability of LR-{\epsilon}NVC, LR-{\epsilon}NVC-R and NN-{\epsilon}NVC. We conduct extensive numerical experiments to compare LR-{\epsilon}NVC-R and NN-{\epsilon}NVC with two existing approaches, estimate-as-solution (EAS) and integrated estimation and optimization (IEO). The results show that LR-{\epsilon}NVC-R and NN-{\epsilon}NVC outperform both EAS and IEO, with maximum cost savings up to 14.40% and 12.21% compared to the lowest cost generated by the two existing approaches. In addition, LR-{\epsilon}NVC-R's and NN-{\epsilon}NVC's order quantities are statistically significantly closer to the optimal solutions should the underlying distribution be known.

We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays. We present a procedure which, for any given $q \in (0,1]$, transforms any standard stochastic first-order method to an asynchronous method with convergence guarantee depending on the $q$-quantile delay of the sequence. This approach leads to convergence rates of the form $O(\tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems, where $\tau_q$ is the $q$-quantile delay, generalizing and improving on existing results that depend on the average delay. We further show a method that automatically adapts to all quantiles simultaneously, without any prior knowledge of the delays, achieving convergence rates of the form $O(\inf_{q} \tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\inf_{q} \tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems. Our technique is based on asynchronous mini-batching with a careful batch-size selection and filtering of stale gradients.

We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent work (Na et al. 2023) demonstrated that Hessian averaging can be utilized to achieve fast $\mathcal{O}\left(\sqrt{\tfrac{\log k}{k}}\right)$ local superlinear convergence for strongly convex functions in high probability, while maintaining fixed per-iteration Hessian costs. These methods, however, require gradient exactness and strong convexity, which poses challenges for their practical implementation. To address this concern we consider Hessian-averaged methods that allow gradient inexactness via norm condition based adaptive-sampling strategies. For the finite-sum problem we utilize deterministic sampling techniques which lead to global linear and sublinear convergence rates for strongly convex and nonconvex functions respectively. In this setting we are able to derive an improved deterministic local superlinear convergence rate of $\mathcal{O}\left(\tfrac{1}{k}\right)$. For the %expected risk expectation problem we utilize stochastic sampling techniques, and derive global linear and sublinear rates for strongly convex and nonconvex functions, as well as a $\mathcal{O}\left(\tfrac{1}{\sqrt{k}}\right)$ local superlinear convergence rate, all in expectation. We present novel analysis techniques that differ from the previous probabilistic results. Additionally, we propose scalable and efficient variations of these methods via diagonal approximations and derive the novel diagonally-averaged Newton (Dan) method for large-scale problems. Our numerical results demonstrate that the Hessian averaging not only helps with convergence, but can lead to state-of-the-art performance on difficult problems such as CIFAR100 classification with ResNets.

Recently, a sparse version of Student-t Processes, termed sparse variational Student-t Processes, has been proposed to enhance computational efficiency and flexibility for real-world datasets using stochastic gradient descent. However, traditional gradient descent methods like Adam may not fully exploit the parameter space geometry, potentially leading to slower convergence and suboptimal performance. To mitigate these issues, we adopt natural gradient methods from information geometry for variational parameter optimization of Student-t Processes. This approach leverages the curvature and structure of the parameter space, utilizing tools such as the Fisher information matrix which is linked to the Beta function in our model. This method provides robust mathematical support for the natural gradient algorithm when using Student's t-distribution as the variational distribution. Additionally, we present a mini-batch algorithm for efficiently computing natural gradients. Experimental results across four benchmark datasets demonstrate that our method consistently accelerates convergence speed.

Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted version of the Bayesian GPLVMs has been proposed to obtain a tighter variational bound. However, this version of the approach is primarily limited to analyzing simple data structures, as the generation of an effective proposal distribution can become quite challenging in high-dimensional spaces or with complex data sets. In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. By transforming the posterior into a sequence of intermediate distributions using annealing, we combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. We further propose an efficient algorithm by reparameterizing all variables in the evidence lower bound (ELBO). Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.