Humans and other animals are capable of improving their learning performance as they solve related tasks from a given problem domain, to the point of being able to learn from extremely limited data. While synaptic plasticity is generically thought to underlie learning in the brain, the precise neural and synaptic mechanisms by which learning processes improve through experience are not well understood. Here, we present a general-purpose, biologically-plausible meta-learning rule which estimates gradients with respect to the parameters of an underlying learning algorithm by simply running it twice. Our rule may be understood as a generalization of contrastive Hebbian learning to meta-learning and notably, it neither requires computing second derivatives nor going backwards in time, two characteristic features of previous gradient-based methods that are hard to conceive in physical neural circuits. We demonstrate the generality of our rule by applying it to two distinct models: a complex synapse with internal states which consolidate task-shared information, and a dual-system architecture in which a primary network is rapidly modulated by another one to learn the specifics of each task. For both models, our meta-learning rule matches or outperforms reference algorithms on a wide range of benchmark problems, while only using information presumed to be locally available at neurons and synapses. We corroborate these findings with a theoretical analysis of the gradient estimation error incurred by our rule.

We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs.

We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case performance and worst-case instance of first-order optimization methods by solving an SDP. Unlike previous work, the size of our new PEP formulation is independent of the network size. For this purpose, we take a global view of the decentralized problem and we also decouple the consensus subspace and its orthogonal complement. We apply our methodology to different decentralized methods such as DGD, DIGing and EXTRA and obtain numerically tight performance guarantees that are valid for any network size.

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties of the originally given graph. Graph data consist of node features and graph matrix (e.g., adjacency and Laplacian). The existing graph coarsening methods ignore the node features and rely solely on a graph matrix to simplify graphs. In this paper, we introduce a novel optimization-based framework for graph dimensionality reduction. The proposed framework lies in the unification of graph learning and dimensionality reduction. It takes both the graph matrix and the node features as the input and learns the coarsen graph matrix and the coarsen feature matrix jointly while ensuring desired properties. The proposed optimization formulation is a multi-block non-convex optimization problem, which is solved efficiently by leveraging block majorization-minimization, $\log$ determinant, Dirichlet energy, and regularization frameworks. The proposed algorithms are provably convergent and practically amenable to numerous tasks. It is also established that the learned coarsened graph is $\epsilon\in(0,1)$ similar to the original graph. Extensive experiments elucidate the efficacy of the proposed framework for real-world applications.

Stochastic convex optimization is a well-studied area with numerous applications in algorithms, machine learning, and beyond. Various algorithms have been shown to converge for many classes of functions including Lipschitz functions, smooth functions, and their linear combinations. However, one curious gap remains in the understanding of their convergence with high probability compared with convergence in expectation. Classical results show that in expectation, the function value gap of the final solution is proportional to the distance between the original solution and the optimal solution. On the other hand, classical results for convergence with high probability could only show that the function value gap of the final solution is proportional to the diameter of the domain, which could be much larger or even unbounded.

In Bayesian optimization (BO) for expensive black-box optimization tasks, acquisition function (AF) guides sequential sampling and plays a pivotal role for efficient convergence to better optima. Prevailing AFs usually rely on artificial experiences in terms of preferences for exploration or exploitation, which runs a risk of a computational waste or traps in local optima and resultant re-optimization. To address the crux, the idea of data-driven AF selection is proposed, and the sequential AF selection task is further formalized as a Markov decision process (MDP) and resort to powerful reinforcement learning (RL) technologies. Appropriate selection policy for AFs is learned from superior BO trajectories to balance between exploration and exploitation in real time, which is called reinforcement-learning-assisted Bayesian optimization (RLABO). Competitive and robust BO evaluations on five benchmark problems demonstrate RL's recognition of the implicit AF selection pattern and imply the proposal's potential practicality for intelligent AF selection as well as efficient optimization in expensive black-box problems.

When solving a real-world optimization problem we often have no information about the analytic form of the objective function. Evaluation of such black-box functions is frequently expensive in terms of time and money (Baerns and Holeňa, 2009; Lee et al., 2016; Zaefferer et al., 2016), which has been for two decades the driving force of research into surrogate modeling of black-box objective functions (Büche et al., 2005; Forrester and Keane, 2009; Jin, 2011). Given a set of observations, a surrogate model can be fitted to approximate the landscape of the black-box function. The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) by Hansen (2006), which we consider the state-of-the-art evolutionary black-box optimizer, has been frequently combined with surrogate models.

As humans, we perceive the three-dimensional structure of the world around us with apparent ease. Think of how vivid the three-dimensional percept is when you look at a vase of flowers sitting on the table next to you. You can tell the shape and translucency of each petal through the subtle patterns of light and shading that play across its surface and effortlessly segment each flower from the background of the scene (Figure 1.1). Looking at a framed group por- trait, you can easily count (and name) all of the people in the picture and even guess at their emotions from their facial appearance. Perceptual psychologists have spent decades trying to understand how the visual system works and, even though they can devise optical illusions1 to tease apart some of its principles (Figure 1.3), a complete solution to this puzzle remains elusive (Marr 1982; Palmer 1999; Livingstone 2008).

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared.

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems. However, the computation of Bayesian posteriors is typically an intractable problem, and has spawned a large literature on approximate Bayesian computation. Here, in the context of chance-constrained optimization, we focus on the question of statistical consistency (in an appropriate sense) of the optimal value, computed using an approximate posterior distribution. To this end, we rigorously prove a frequentist consistency result demonstrating the convergence of the optimal value to the optimal value of a fixed, parameterized constrained optimization problem. We augment this by also establishing a probabilistic rate of convergence of the optimal value. We also prove the convex feasibility of the approximate Bayesian stochastic optimization problem. Finally, we demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queueing model.