In this work, we consider one challenging training time attack by modifying training data with bounded perturbation, hoping to manipulate the behavior (both targeted or non-targeted) of any corresponding trained classifier during test time when facing clean samples. To achieve this, we proposed to use an auto-encoder-like network to generate such adversarial perturbations on the training data together with one imaginary victim differentiable classifier. The perturbation generator will learn to update its weights so as to produce the most harmful noise, aiming to cause the lowest performance for the victim classifier during test time. This can be formulated into a non-linear equality constrained optimization problem. Unlike GANs, solving such problem is computationally challenging, we then proposed a simple yet effective procedure to decouple the alternating updates for the two networks for stability.

Stochastic classifiers arise in a number of machine learning problems, and have become especially prominent of late, as they often result from constrained optimization problems, e.g. for fairness, churn, or custom losses. Despite their utility, the inherent randomness of stochastic classifiers may cause them to be problematic to use in practice for a variety of practical reasons. In this paper, we attempt to answer the theoretical question of how well a stochastic classifier can be approximated by a deterministic one, and compare several different approaches, proving lower and upper bounds. We also experimentally investigate the pros and cons of these methods, not only in regard to how successfully each deterministic classifier approximates the original stochastic classifier, but also in terms of how well each addresses the other issues that can make stochastic classifiers undesirable. Papers published at the Neural Information Processing Systems Conference.

Expected improvement and other acquisition functions widely used in Bayesian optimization use a "one-step" assumption: they value objective function evaluations assuming no future evaluations will be performed. Because we usually evaluate over multiple steps, this assumption may leave substantial room for improvement. Existing theory gives acquisition functions looking multiple steps in the future but calculating them requires solving a high-dimensional continuous-state continuous-action Markov decision process (MDP). Fast exact solutions of this MDP remain out of reach of today's methods. As a result, previous two- and multi-step lookahead Bayesian optimization algorithms are either too expensive to implement in most practical settings or resort to heuristics that may fail to fully realize the promise of two-step lookahead.

We consider a decentralized learning problem, where a set of computing nodes aim at solving a non-convex optimization problem collaboratively. It is well-known that decentralized optimization schemes face two major system bottlenecks: stragglers' delay and communication overhead. In this paper, we tackle these bottlenecks by proposing a novel decentralized and gradient-based optimization algorithm named as QuanTimed-DSGD. Our algorithm stands on two main ideas: (i) we impose a deadline on the local gradient computations of each node at each iteration of the algorithm, and (ii) the nodes exchange quantized versions of their local models. The key technical contribution of our work is to prove that with non-vanishing noises for quantization and stochastic gradients, the proposed method exactly converges to the global optimal for convex loss functions, and finds a first-order stationary point in non-convex scenarios.

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.

Metamodels offer a cheap statistical representation of complex and/or expensive stochastic simulators that arise in applications ranging from engineering to environmental science and finance [Santner et al., 2013]. Gaussian process (GP) frameworks have emerged as the leading family of metamodels thanks to their flexibility, analytical tractability and superior empirical performance. However, for GP metamodels to be fast, it is imperative to keep the respective design size A manageable. In particular, unless the simulator is truly expensive or the input domain is vast, the typical recommendation is to restrict to hundreds of inputs, A 10 3 . This creates a major tension as frequently the stochastic simulator has low signal-to-noise ratio or a complex noise structure. A prototypical example is where the simulator Y (x) F (X [0, t]) X0 x involves functionals of a continuous-time Markov chain or stochastic differential equation solution (X t), whereby the stochasticity tends to dominate the trend/drift term for short t, and moreover simulation noise is non-Gaussian and state-dependent (heteroskedastic). Both authors are partially supported by NSF DMS-1521743.

In this paper, the problem of minimizing energy and time consumption for task computation and transmission is studied in a mobile edge computing (MEC)-enabled balloon network. In the considered network, each user needs to process a computational task in each time instant, where high-altitude balloons (HABs), acting as flying wireless base stations, can use their powerful computational abilities to process the tasks offloaded from their associated users. Since the data size of each user's computational task varies over time, the HABs must dynamically adjust the user association, service sequence, and task partition scheme to meet the users' needs. This problem is posed as an optimization problem whose goal is to minimize the energy and time consumption for task computing and transmission by adjusting the user association, service sequence, and task allocation scheme. To solve this problem, a support vector machine (SVM)-based federated learning (FL) algorithm is proposed to determine the user association proactively. The proposed SVM-based FL method enables each HAB to cooperatively build an SVM model that can determine all user associations without any transmissions of either user historical associations or computational tasks to other HABs. Given the prediction of the optimal user association, the service sequence and task allocation of each user can be optimized so as to minimize the weighted sum of the energy and time consumption. Simulations with real data of city cellular traffic from the OMNILab at Shanghai Jiao Tong University show that the proposed algorithm can reduce the weighted sum of the energy and time consumption of all users by up to 16.1% compared to a conventional centralized method.

We present a fast search on graph algorithm for Maximum Inner Product Search (MIPS). This optimization problem is challenging since traditional Approximate Nearest Neighbor (ANN) search methods may not perform efficiently in the non-metric similarity measure. Our proposed method is based on the property that Möbius transformation introduces an isomorphism between a subgraph of l 2-Delaunay graph and Delaunay graph for inner product. Under this observation, we propose a simple but novel graph indexing and searching algorithm to find the optimal solution with the largest inner product with the query. Experiments show our approach leads to significant improvements compared to existing methods.

We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto-set of solutions by minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel approach referred to as Max-value Entropy Search for Multi-objective Optimization (MESMO) to solve this problem. MESMO employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation for quickly uncovering high-quality solutions. We also provide theoretical analysis to characterize the efficacy of MESMO.

The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems. However, AdaMM is not suited for solving black-box optimization problems, where explicit gradient forms are difficult or infeasible to obtain. In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime. We show that the convergence rate of ZO-AdaMM for both convex and nonconvex optimization is roughly a factor of $O(\sqrt{d})$ worse than that of the first-order AdaMM algorithm, where $d$ is problem size. In particular, we provide a deep understanding on why Mahalanobis distance matters in convergence of ZO-AdaMM and other AdaMM-type methods.