In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired target performance? Here, we show that the piecewise linear property, very common in everyday neural networks, allows for an inverse design formulation based on mixed-integer linear programming. Our mixed-integer inverse design uncovers globally optimal or near optimal solutions in a principled manner. Furthermore, our method significantly facilitates emerging, but challenging, combinatorial inverse design tasks, such as material selection. For problems where finding the optimal solution is not desirable or tractable, we develop an efficient yet near-optimal hybrid optimization. Eventually, our method is able to find solutions provably robust to possible fabrication perturbations among multiple designs with similar performances.

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.

Proximal Policy Optimization (PPO) methods learn a policy by iteratively performing multiple mini-batch optimization epochs of a surrogate objective with one set of sampled data. Ratio clipping PPO is a popular variant that clips the probability ratios between the target policy and the policy used to collect samples. Ratio clipping yields a pessimistic estimate of the original surrogate objective, and has been shown to be crucial for strong performance. We show in this paper that such ratio clipping may not be a good option as it can fail to effectively bound the ratios. Instead, one can directly optimize the original surrogate objective for multiple epochs; the key is to find a proper condition to early stop the optimization epoch in each iteration. Our theoretical analysis sheds light on how to determine when to stop the optimization epoch, and call the resulting algorithm Early Stopping Policy Optimization (ESPO). We compare ESPO with PPO across many continuous control tasks and show that ESPO significantly outperforms PPO. Furthermore, we show that ESPO can be easily scaled up to distributed training with many workers, delivering strong performance as well.

This article discusses a particular case of the data clustering problem, where it is necessary to find groups of adjacent text segments of the appropriate length that match a fuzzy pattern represented as a sequence of fuzzy properties. To solve this problem, a heuristic algorithm for finding a sufficiently large number of solutions is proposed. The key idea of the proposed algorithm is the use of the prefix structure to track the process of mapping text segments to fuzzy properties. An important special case of the text segmentation problem is the fuzzy string matching problem, when adjacent text segments have unit length and, accordingly, the fuzzy pattern is a sequence of fuzzy properties of text characters. It is proven that the heuristic segmentation algorithm in this case finds all text segments that match the fuzzy pattern. Finally, we consider the problem of a best segmentation of the entire text based on a fuzzy pattern, which is solved using the dynamic programming method.

Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale setting where the number of samples is huge, it is crucial to develop stochastic methods, which only use a few samples at a time to progress. However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates. To overcome this problem we introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. These directions are written as a sum, making it straightforward to derive unbiased estimates. The simplicity of our approach allows us to develop global variance reduction algorithms, where the dynamics of all variables is subject to variance reduction. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has $O(\frac1T)$ convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption. This is the first stochastic algorithm for bilevel optimization that verifies either of these properties. Numerical experiments validate the usefulness of our method.

Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower rate of convergence $O((G/T)^{2/3})$ compared with their uncompressed counterpart, where $G$ measures the data heterogeneity across different clients, and $T$ is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of $O(1/T)$. This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of BEER in the data heterogeneous regime.

Destination prediction has been a critical topic in transportation research, and there are a large number of studies. However, almost all existing studies are based on high predictability data conditions while pay less attention to the data condition with low predictability, where the regularity of single individuals is not exposed. Based on a certain period of observation, there is a fact that individuals may choose destinations beyond observation, which we call "potential destinations". The number of potential destinations is very large and can't be ignored for the data condition with low predictability formed by short-term observation.To reveal the choice pattern of potential destination of individuals under the data condition with low predictability, we propose a global optimization method based on knowledge graph embedding. First, we joint the trip data of all individuals by constructing Trip Knowledge Graph(TKG). Next, we optimize the general algorithm of knowledge graph embedding for our data and task in training strategy and objective function, then implement it on TKG. It can achieve global optimization for association paths that exist between almost any two entities in TKG. On this basis, a method for potential destination prediction is proposed, giving the possible ranking of unobserved destinations for each individual. In addition, we improve the performance by fusing static statistical information that is not passed to TKG. Finally, we validate our method in a real-world dataset, and the prediction results are highly consistent with individuals' potential destination choice behaviour.

We focus on parameterized policy search for reinforcement learning over continuous action spaces. Typically, one assumes the score function associated with a policy is bounded, which fails to hold even for Gaussian policies. To properly address this issue, one must introduce an exploration tolerance parameter to quantify the region in which it is bounded. Doing so incurs a persistent bias that appears in the attenuation rate of the expected policy gradient norm, which is inversely proportional to the radius of the action space. To mitigate this hidden bias, heavy-tailed policy parameterizations may be used, which exhibit a bounded score function, but doing so can cause instability in algorithmic updates. To address these issues, in this work, we study the convergence of policy gradient algorithms under heavy-tailed parameterizations, which we propose to stabilize with a combination of mirror ascent-type updates and gradient tracking. Our main theoretical contribution is the establishment that this scheme converges with constant step and batch sizes, whereas prior works require these parameters to respectively shrink to null or grow to infinity. Experimentally, this scheme under a heavy-tailed policy parameterization yields improved reward accumulation across a variety of settings as compared with standard benchmarks.

We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.