Online optimization is a well-established optimization paradigm that aims to make a sequence of correct decisions given knowledge of the correct answer to previous decision tasks. Bilevel programming involves a hierarchical optimization problem where the feasible region of the so-called outer problem is restricted by the graph of the solution set mapping of the inner problem. This paper brings these two ideas together and studies an online bilevel optimization setting in which a sequence of time-varying bilevel problems are revealed one after the other. We extend the known regret bounds for single-level online algorithms to the bilevel setting. Specifically, we introduce new notions of bilevel regret, develop an online alternating time-averaged gradient method that is capable of leveraging smoothness, and provide regret bounds in terms of the path-length of the inner and outer minimizer sequences.

Bilevel optimization plays an essential role in many machine learning tasks, ranging from hyperparameter optimization to meta-learning. Existing studies on bilevel optimization, however, focus on either centralized or synchronous distributed setting. The centralized bilevel optimization approaches require collecting a massive amount of data to a single server, which inevitably incur significant communication expenses and may give rise to data privacy risks. Synchronous distributed bilevel optimization algorithms, on the other hand, often face the straggler problem and will immediately stop working if a few workers fail to respond. As a remedy, we propose A synchronous D istributed Bilevel O ptimization (ADBO) algorithm. The proposed ADBO can tackle bilevel optimization problems with both nonconvex upper-level and lower-level objective functions, and its convergence is theoretically guaranteed. In bilevel optimization, one optimization problem is embedded or nested with another. Specifically, the outer optimization problem is called the upper-level optimization problem and the inner optimization problem is called the lower-level optimization problem.

We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter tailored to prioritized non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-squares programming via a globally convergent sequential quadratic programming step-filter. Leveraging a condition on the trust-region or the filter initialization, our hierarchical step-filter maintains this global convergence property. The hierarchical least-squares programming sub-problems are solved via a sparse nullspace method based interior point method. It is based on an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. It is also here that we propose a nullspace trust region adaptation method towards a comprehensive hierarchical step-filter. We demonstrate the computational efficiency of the hierarchical solver on typical test functions like the Rosenbrock and Himmelblau's functions, inverse kinematics problems and optimal control.

In Bayesian optimisation, we often seek to minimise the black-box objective functions that arise in real-world physical systems. A primary contributor to the cost of evaluating such black-box objective functions is often the effort required to prepare the system for measurement. We consider a common scenario where preparation costs grow as the distance between successive evaluations increases. In this setting, smooth optimisation trajectories are preferred and the jumpy paths produced by the standard myopic (i.e.\ one-step-optimal) Bayesian optimisation methods are sub-optimal. Our algorithm, MONGOOSE, uses a meta-learnt parametric policy to generate smooth optimisation trajectories, achieving performance gains over existing methods when optimising functions with large movement costs.

Model Predictive Path Integral (MPPI) control is a type of sampling-based model predictive control that simulates thousands of trajectories and uses these trajectories to synthesize optimal controls on-the-fly. In practice, however, MPPI encounters problems limiting its application. For instance, it has been observed that MPPI tends to make poor decisions if unmodeled dynamics or environmental disturbances exist, preventing its use in safety-critical applications. Moreover, the multi-threaded simulations used by MPPI require significant onboard computational resources, making the algorithm inaccessible to robots without modern GPUs. To alleviate these issues, we propose a novel (Shield-MPPI) algorithm that provides robustness against unpredicted disturbances and achieves real-time planning using a much smaller number of parallel simulations on regular CPUs. The novel Shield-MPPI algorithm is tested on an aggressive autonomous racing platform both in simulation and using experiments. The results show that the proposed controller greatly reduces the number of constraint violations compared to state-of-the-art robust MPPI variants and stochastic MPC methods.

A recourse action aims to explain a particular algorithmic decision by showing one specific way in which the instance could be modified to receive an alternate outcome. Existing recourse generation methods often assume that the machine learning model does not change over time. However, this assumption does not always hold in practice because of data distribution shifts, and in this case, the recourse action may become invalid. To redress this shortcoming, we propose the Distributionally Robust Recourse Action (DiRRAc) framework, which generates a recourse action that has a high probability of being valid under a mixture of model shifts. We formulate the robustified recourse setup as a min-max optimization problem, where the max problem is specified by Gelbrich distance over an ambiguity set around the distribution of model parameters. Then we suggest a projected gradient descent algorithm to find a robust recourse according to the min-max objective. We show that our DiRRAc framework can be extended to hedge against the misspecification of the mixture weights. Numerical experiments with both synthetic and three real-world datasets demonstrate the benefits of our proposed framework over state-of-the-art recourse methods.

One of the most crucial and challenging steps in the development of robots intended to restore the mobility of the human body after a loss of functional movement due to neurological injuries is the IK of physiological limbs, which consists of computing joint angles configuration based on the predefined input workspace coordinates. Generally speaking, the complexity of the IK problem depends on the geometry of the manipulator and the nonlinearity of its model, which gives the corresponding relation between the task and the joint spaces. Furthermore, IK solution is essential for the real-time control. Thus, it must be precise in order to enable the robot to perform the task successfully. IK techniques can be classified into three categories, namely, analytical method, numerical method, and intelligent method. The analytical method solves IK by solving a set of closed-form equations that can give the generalized coordinate value that drives the end effector of the manipulator to the predefined target position [1].

Current embedded systems are specifically designed to run multimedia applications. These applications have a big impact on both performance and energy consumption. Both metrics can be optimized selecting the best cache configuration for a target set of applications. Multi-objective optimization may help to minimize both conflicting metrics in an independent manner. In this work, we propose an optimization method that based on Multi-Objective Evolutionary Algorithms, is able to find the best cache configuration for a given set of applications. To evaluate the goodness of candidate solutions, the execution of the optimization algorithm is combined with a static profiling methodology using several well-known simulation tools. Results show that our optimization framework is able to obtain an optimized cache for Mediabench applications. Compared to a baseline cache memory, our design method reaches an average improvement of 64.43\% and 91.69\% in execution time and energy consumption, respectively.

Rapidly exploring random trees (RRTs) have proven effective in quickly finding feasible solutions to complex motion planning problems. RRT* is an extension of the RRT algorithm that provides probabilistic asymptotic optimality guarantees when using straight-line motion primitives. This work provides extensions to RRT and RRT* that employ fillets as motion primitives, allowing path curvature constraints to be considered when planning. Two fillets are developed, an arc-based fillet that uses circular arcs to generate paths that respect maximum curvature constraints and a spline-based fillet that uses Bezier curves to additionally respect curvature continuity requirements. Planning with these fillets is shown to far exceed the performance of RRT* using Dubin's path motion primitives, approaching the performance of planning with straight-line path primitives. Path sampling heuristics are also introduced to accelerate convergence for nonholonomic motion planning. Comparisons to established RRT* approaches are made using the Open Motion Planning Library (OMPL).

As machine learning being used increasingly in making high-stakes decisions, an arising challenge is to avoid unfair AI systems that lead to discriminatory decisions for protected population. A direct approach for obtaining a fair predictive model is to train the model through optimizing its prediction performance subject to fairness constraints, which achieves Pareto efficiency when trading off performance against fairness. Among various fairness metrics, the ones based on the area under the ROC curve (AUC) are emerging recently because they are threshold-agnostic and effective for unbalanced data. In this work, we formulate the training problem of a fairness-aware machine learning model as an AUC optimization problem subject to a class of AUC-based fairness constraints. This problem can be reformulated as a min-max optimization problem with min-max constraints, which we solve by stochastic first-order methods based on a new Bregman divergence designed for the special structure of the problem. We numerically demonstrate the effectiveness of our approach on real-world data under different fairness metrics.