Over the last decade, differential privacy has evolved from a rigorous paradigm derived by theoretical computer scientists for releasing sensitive data to a technology deployed at scale in numerous applications [Ding et al., 2017, Erlingsson et al., 2014, Garfinkel et al., 2019, Tang et al., 2017]. The setting assumes the existence of a trusted curator who holds the data of individuals in a database, and the goal of privacy is to simultaneously protect individual data while allowing statistical analysis of the aggregate database. Such protection is guaranteed by differential privacy in the context of a remote access query system, where a statistician can only indirectly access the data, e.g., by obtaining noisy summary statistics or outputs of a model. Injecting noise before releasing information to the statistician is essential for preserving privacy, and the noise should be as small as possible in order to optimize statistical performance of the released statistics. In this paper, we consider the problem of estimation and inference for M-estimators. Inspired by the work of Bassily et al. [2014], Lee and Kifer [2018], Song et al. [2013], and Feldman et al. [2020], among others, we propose noisy optimization procedures that output differentially private counterparts of standard M-estimators. The central idea of these methods is to add noise to every iterate of a gradient-based optimization routine in a way that causes each iterate to satisfy a targeted differential privacy guarantee.

In dense and dynamic scenarios, planning a safe and comfortable trajectory is full of challenges when traffic participants are driving at high speed. The classic graph search and sampling methods first perform path planning and then configure the corresponding speed, which lacks a strategy to deal with the high-speed obstacles. Decoupling optimization methods perform motion planning in the S-L and S-T domains respectively. These methods require a large free configuration space to plan the lane change trajectory. In dense dynamic scenes, it is easy to cause the failure of trajectory planning and be cut in by others, causing slow driving speed and bring safety hazards. We analyze the collision relationship in the spatio-temporal domain, and propose an instantaneous analysis model which only analyzes the collision relationship at the same time. In the model, the collision-free constraints in 3D spatio-temporal domain is projected to the 2D space domain to remove redundant constraints and reduce computational complexity. Experimental results show that our method can plan a safe and comfortable lane-changing trajectory in dense dynamic scenarios. At the same time, it improves traffic efficiency and increases ride comfort.

There are numerous examples in machine learning, statistics, mathematics and deep learning, requiring an algorithm to solve some complicated equations: for instance, maximum likelihood estimation (think about logistic regression or the EM algorithm) or gradient methods (think about stochastic or swarm optimization). Here we are dealing with even more difficult problems, where the solution is not a set of optimal parameters (a finite dimensional object), but a function (an infinite dimensional object). The context is discrete, chaotic dynamical systems, with applications to weather forecasting, population growth models, complex econometric systems, image encryption, chemistry (mixtures), physics (how matter reaches an equilibrium temperature), astronomy (how celestial man-made or natural bodies end up having stable or unstable orbits), or stock market prices, to name a few. These are referred to as complex systems. The solutions to the problems discussed here requires numerical methods, as usually no exact solution is known.

A kitchen assistant needs to operate human-scale objects, such as cabinets and ovens, in unmapped environments with dynamic obstacles. Autonomous interactions in such real-world environments require integrating dexterous manipulation and fluid mobility. While mobile manipulators in different form-factors provide an extended workspace, their real-world adoption has been limited. This limitation is in part due to two main reasons: 1) inability to interact with unknown human-scale objects such as cabinets and ovens, and 2) inefficient coordination between the arm and the mobile base. Executing a high-level task for general objects requires a perceptual understanding of the object as well as adaptive whole-body control among dynamic obstacles. In this paper, we propose a two-stage architecture for autonomous interaction with large articulated objects in unknown environments. The first stage uses a learned model to estimate the articulated model of a target object from an RGB-D input and predicts an action-conditional sequence of states for interaction. The second stage comprises of a whole-body motion controller to manipulate the object along the generated kinematic plan. We show that our proposed pipeline can handle complicated static and dynamic kitchen settings. Moreover, we demonstrate that the proposed approach achieves better performance than commonly used control methods in mobile manipulation. For additional material, please check: https://www.pair.toronto.edu/articulated-mm/ .

The partial Latin square extension problem is to fill as many as possible empty cells of a partially filled Latin square. This problem is a useful model for a wide range of relevant applications in diverse domains. This paper presents the first massively parallel hybrid search algorithm for this computationally challenging problem based on a transformation of the problem to partial graph coloring. The algorithm features the following original elements. Based on a very large population (with more than $10^4$ individuals) and modern graphical processing units, the algorithm performs many local searches in parallel to ensure an intensified exploitation of the search space. It employs a dedicated crossover with a specific parent matching strategy to create a large number of diversified and information-preserving offspring at each generation. Extensive experiments on 1800 benchmark instances show a high competitiveness of the algorithm compared with the current best performing methods. Competitive results are also reported on the related Latin square completion problem. Analyses are performed to shed lights on the understanding of the main algorithmic components. The code of the algorithm will be made publicly available.

We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state EAs. For the standard bimodal benchmark function \twomax we rigorously prove that using uniform parent selection leads to exponential runtimes with high probability to locate both optima for the standard ($\mu$+1)~EA and ($\mu$+1)~RLS with any polynomial population sizes. On the other hand, we prove that selecting the worst individual as parent leads to efficient global optimisation with overwhelming probability for reasonable population sizes. Since always selecting the worst individual may have detrimental effects for escaping from local optima, we consider the performance of stochastic parent selection operators with low selective pressure for a function class called \textsc{TruncatedTwoMax} where one slope is shorter than the other. An experimental analysis shows that the EAs equipped with inverse tournament selection, where the loser is selected for reproduction and small tournament sizes, globally optimise \textsc{TwoMax} efficiently and effectively escape from local optima of \textsc{TruncatedTwoMax} with high probability. Thus they identify both optima efficiently while uniform (or stronger) selection fails in theory and in practice. We then show the power of inverse selection on function classes from the literature where populations are essential by providing rigorous proofs or experimental evidence that it outperforms uniform selection equipped with or without a restart strategy. We conclude the paper by confirming our theoretical insights with an empirical analysis of the different selective pressures on standard benchmarks of the classical MaxSat and Multidimensional Knapsack Problems.

We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of parallel trials. This is a typical scenario when optimizing variable settings that are very costly to evaluate, for example in the context of simulation-based optimization or machine learning hyperparameterization. We propose an original method that uses established approaches to propose a set of points for each batch and then down-selects from these candidate points to the number of trials that can be run in parallel. The key novelty of our approach lies in the introduction of a hyperparameterized method for down-selecting the number of candidates to the allowed batch-size, which is optimized offline using automated algorithm configuration. We tune this method for black box optimization and then evaluate on classical black box optimization benchmarks. Our results show that it is possible to learn how to combine evaluation points suggested by highly diverse black box optimization methods conditioned on the progress of the optimization. Compared with the state of the art in black box minimization and various other methods specifically geared towards few-shot minimization, we achieve an average reduction of 50\% of normalized cost, which is a highly significant improvement in performance.

Since its introduction a decade ago, \emph{relative entropy policy search} (REPS) has demonstrated successful policy learning on a number of simulated and real-world robotic domains, not to mention providing algorithmic components used by many recently proposed reinforcement learning (RL) algorithms. While REPS is commonly known in the community, there exist no guarantees on its performance when using stochastic and gradient-based solvers. In this paper we aim to fill this gap by providing guarantees and convergence rates for the sub-optimality of a policy learned using first-order optimization methods applied to the REPS objective. We first consider the setting in which we are given access to exact gradients and demonstrate how near-optimality of the objective translates to near-optimality of the policy. We then consider the practical setting of stochastic gradients, and introduce a technique that uses \emph{generative} access to the underlying Markov decision process to compute parameter updates that maintain favorable convergence to the optimal regularized policy.

In the family of Intelligent Transportation Systems (ITS), Multimodal Transport Systems (MMTS) have placed themselves as a mainstream transportation mean of our time as a feasible integrative transportation process. The Global Economy progressed with the help of transportation. The volume of goods and distances covered have doubled in the last ten years, so there is a high demand of an optimized transportation, fast but with low costs, saving resources but also safe, with low or zero emissions. Thus, it is important to have an overview of existing research in this field, to know what was already done and what is to be studied next. The main objective is to explore a beneficent selection of the existing research, methods and information in the field of multimodal transportation research, to identify industry needs and gaps in research and provide context for future research. The selective survey covers multimodal transport design and optimization in terms of: cost, time, and network topology. The multimodal transport theoretical aspects, context and resources are also covering various aspects. The survey's selection includes nowadays best methods and solvers for Intelligent Transportation Systems (ITS). The gap between theory and real-world applications should be further solved in order to optimize the global multimodal transportation system.

Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models and non-convex problems are considered, strong simplifying assumptions are often made to make Hessian spectral analysis more tractable. This leads to the question of how relevant the conclusions of such analyses are for more realistic nonlinear models. In this paper, we exploit deterministic equivalent techniques from random matrix theory to make a \emph{precise} characterization of the Hessian eigenspectra for a broad family of nonlinear models, including models that generalize the classical generalized linear models, without relying on strong simplifying assumptions used previously. We show that, depending on the data properties, the nonlinear response model, and the loss function, the Hessian can have \emph{qualitatively} different spectral behaviors: of bounded or unbounded support, with single- or multi-bulk, and with isolated eigenvalues on the left- or right-hand side of the bulk. By focusing on such a simple but nontrivial nonlinear model, our analysis takes a step forward to unveil the theoretical origin of many visually striking features observed in more complex machine learning models.