Balancing performance and safety is crucial to deploying autonomous vehicles in multi-agent environments. In particular, autonomous racing is a domain that penalizes safe but conservative policies, highlighting the need for robust, adaptive strategies. Current approaches either make simplifying assumptions about other agents or lack robust mechanisms for online adaptation. This work makes algorithmic contributions to both challenges. First, to generate a realistic, diverse set of opponents, we develop a novel method for self-play based on replica-exchange Markov chain Monte Carlo. Second, we propose a distributionally robust bandit optimization procedure that adaptively adjusts risk aversion relative to uncertainty in beliefs about opponents' behaviors. We rigorously quantify the tradeoffs in performance and robustness when approximating these computations in real-time motion-planning, and we demonstrate our methods experimentally on autonomous vehicles that achieve scaled speeds comparable to Formula One racecars.

We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This is an unsupervised way to learn general-purpose graph representations, it can be used for both graph sketching and graph comparison. COPT involves simultaneously optimizing dual transport plans, one between the vertices of two graphs, and another between graph signal probability distributions. We show both theoretically and empirically that our method preserves important global structural information on graphs, in particular spectral information, making it well-suited for tasks on graphs including retrieval, classification, summarization, and visualization.

Many real-world applications can be modelled as complex networks, and such networks include the Internet, epidemic disease networks, transport networks, power grids, protein-folding structures and others. Network integrity and robustness are important to ensure that crucial networks are protected and undesired harmful networks can be dismantled. Network structure and integrity can be controlled by a set of key nodes, and to find the optimal combination of nodes in a network to ensure network structure and integrity can be an NP-complete problem. Despite extensive studies, existing methods have many limitations and there are still many unresolved problems. This paper presents a probabilistic approach based on neighborhood information and node importance, namely, neighborhood information-based probabilistic algorithm (NIPA). We also define a new centrality-based importance measure (IM), which combines the contribution ratios of the neighbor nodes of each target node and two-hop node information. Our proposed NIPA has been tested for different network benchmarks and compared with three other methods: optimal attack strategy (OAS), high betweenness first (HBF) and high degree first (HDF). Experiments suggest that the proposed NIPA is most effective among all four methods. In general, NIPA can identify the most crucial node combination with higher effectiveness, and the set of optimal key nodes found by our proposed NIPA is much smaller than that by heuristic centrality prediction. In addition, many previously neglected weakly connected nodes are identified, which become a crucial part of the newly identified optimal nodes. Thus, revised strategies for protection are recommended to ensure the safeguard of network integrity. Further key issues and future research topics are also discussed.

Companies spend millions of dollars on their Cloud performance. Much of this is overspend, but large enterprises cannot risk downtime, and so they hugely over-provision in order to buy peace of mind. In this article, we'll reveal how AI-based Continuous Optimization can put a stop to this wastage, and employ automated Machine Learning to help companies save up to 70% on their spend. One of FinOps' objectives has always been to enable shifts in companies and organizations – shifts that empower teams to participate in the process of increasing efficiency, optimizing utilization and reducing spend – through a combination of systems, best practices, and culture. An effective FinOps stance cannot be adopted if a company's applications are habitually running hot because, in such a scenario, a company is not managing its Cloud finances well.

We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.

Stochastic version of alternating direction method of multiplier (ADMM) and its variants (linearized ADMM, gradient-based ADMM) plays a key role for modern large scale machine learning problems. One example is the regularized empirical risk minimization problem. In this work, we put different variants of stochastic ADMM into a unified form, which includes standard, linearized and gradient-based ADMM with relaxation, and study their dynamics via a continuous-time model approach. We adapt the mathematical framework of stochastic modified equation (SME), and show that the dynamics of stochastic ADMM is approximated by a class of stochastic differential equations with small noise parameters in the sense of weak approximation. The continuous-time analysis would uncover important analytical insights into the behaviors of the discrete-time algorithm, which are non-trivial to gain otherwise. For example, we could characterize the fluctuation of the solution paths precisely, and decide optimal stopping time to minimize the variance of solution paths.

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their convergence, which is not affordable for practical applications since the most of them are computationally expensive. In other words, these problems are not only large-scale but also computationally expensive, that makes them very difficult to solve. There is no efficient surrogate model to support large-scale expensive global optimization (LSEGO) problems. As a result, the algorithms should address LSEGO problems using a limited computational budget to be applicable in real-world applications. In this paper, we propose a simple novel algorithm called Shahryar Origami Optimization (SOO) algorithm to tackle LSEGO problems with a limited computational budget. Our proposed algorithm benefits from two leading steps, namely, finding the region of interest and then shrinkage of the search space by folding it into the half with exponential speed. One of the main advantages of the proposed algorithm is being free of any control parameters, which makes it far from the intricacies of the tuning process. The proposed algorithm is compared with cooperative co-evolution with delta grouping on 20 benchmark functions with dimension 1000. Also, we conducted some experiments on CEC-2017, D=10, 30, 50, and 100 to investigate the behavior of SOO algorithm in lower dimensions. The results show that SOO is beneficial not only in large-scale problems, but also in low-scale optimization problems.

We study a novel variant of the multi-armed bandit problem, where at each time step, the player observes a context that determines the arms' mean rewards. However, playing an arm blocks it (across all contexts) for a fixed number of future time steps. This model extends the blocking bandits model (Basu et al., NeurIPS19) to a contextual setting, and captures important scenarios such as recommendation systems or ad placement with diverse users, and processing diverse pool of jobs. This contextual setting, however, invalidates greedy solution techniques that are effective for its non-contextual counterpart. Assuming knowledge of the mean reward for each arm-context pair, we design a randomized LP-based algorithm which is $\alpha$-optimal in (large enough) $T$ time steps, where $\alpha = \tfrac{d_{\max}}{2d_{\max}-1}\left(1- \epsilon\right)$ for any $\epsilon >0$, and $d_{max}$ is the maximum delay of the arms. In the bandit setting, we show that a UCB based variant of the above online policy guarantees $\mathcal{O}\left(\log T\right)$ regret w.r.t. the $\alpha$-optimal strategy in $T$ time steps, which matches the $\Omega(\log(T))$ regret lower bound in this setting. Due to the time correlation caused by the blocking of arms, existing techniques for upper bounding regret fail. As a first, in the presence of such temporal correlations, we combine ideas from coupling of non-stationary Markov chains and opportunistic sub-sampling with suboptimality charging techniques from combinatorial bandits to prove our regret upper bounds.

Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment choices to be made, imposing constraints on the collection of feasible assortments gives more flexibility to incorporate insights of store-managers and historically well-performing assortments. We design fast and flexible algorithms based on variations of binary search that find the revenue of the (approximately) optimal assortment. In particular, we revisit the problem of large-scale assortment optimization under the multinomial logit choice model without any assumptions on the structure of the feasible assortments. We speed up the comparisons steps using novel vector space embeddings, based on advances in the fields of information retrieval and machine learning. For an arbitrary collection of assortments, our algorithms can find a solution in time that is sub-linear in the number of assortments and for the simpler case of cardinality constraints - linear in the number of items (existing methods are quadratic or worse). Empirical validations using the Billion Prices dataset and several retail transaction datasets show that our algorithms are competitive even when the number of items is $\sim 10^5$ ($100$x larger instances than previously studied).

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian Optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists in a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches.