We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem in terms of probability distributions, rather than variational gates. In this framework, the optimal configuration is found by optimizing over distribution parameters, rather than over free angles. We show numerically that this approach can be more competitive than gradient-free methods, for a comparable amount of resources, both for noiseless and noisy circuits. Another interesting feature of this approach to variational compilation is that it does not need a separate register and long-range interactions to estimate the end-point fidelity, which is an improvement over methods which rely on the Hilbert-Schmidt test. We expect these techniques to be relevant for training variational circuits in other contexts.

Ensemble learning has gained success in machine learning with major advantages over other learning methods. Bagging is a prominent ensemble learning method that creates subgroups of data, known as bags, that are trained by individual machine learning methods such as decision trees. Random forest is a prominent example of bagging with additional features in the learning process. Evolutionary algorithms have been prominent for optimisation problems and also been used for machine learning. Evolutionary algorithms are gradient-free methods that work with a population of candidate solutions that maintain diversity for creating new solutions. In conventional bagged ensemble learning, the bags are created once and the content, in terms of the training examples, are fixed over the learning process. In our paper, we propose evolutionary bagged ensemble learning, where we utilise evolutionary algorithms to evolve the content of the bags in order to iteratively enhance the ensemble by providing diversity in the bags. The results show that our evolutionary ensemble bagging method outperforms conventional ensemble methods (bagging and random forests) for several benchmark datasets under certain constraints. We find that evolutionary bagging can inherently sustain a diverse set of bags without reduction in performance accuracy.

We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The position of the precision motion stage is predicted with data-driven models, a linear low-fidelity model is used to optimize traversal time, by changing the path velocity and acceleration profiles then a non-linear high-fidelity model is used to refine the previously found time-optimal solution. We experimentally demonstrate that the proposed method is capable of simultaneously improving the productivity and accuracy of a high precision motion stage. Given the data-based nature of the models, the proposed method can easily be adapted to a wide family of precision motion systems.

Adaptive gradient algorithms such as ADAGRAD and its variants have gained popularity in the training of deep neural networks. While many works as for adaptive methods have focused on the static regret as a performance metric to achieve a good regret guarantee, the dynamic regret analyses of these methods remain unclear. As opposed to the static regret, dynamic regret is considered to be a stronger concept of performance measurement in the sense that it explicitly elucidates the non-stationarity of the environment. In this paper, we go through a variant of ADAGRAD (referred to as M-ADAGRAD ) in a strong convex setting via the notion of dynamic regret, which measures the performance of an online learner against a reference (optimal) solution that may change over time. We demonstrate a regret bound in terms of the path-length of the minimizer sequence that essentially reflects the non-stationarity of environments. In addition, we enhance the dynamic regret bound by exploiting the multiple accesses of the gradient to the learner in each round. Empirical results indicate that M-ADAGRAD works also well in practice.

Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.

Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function; (2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework.

Several Artificial Intelligence based heuristic and metaheuristic algorithms have been developed so far. These algorithms have shown their superiority towards solving complex problems from different domains. However, it is necessary to critically validate these algorithms for solving real-world constrained optimization problems. The search behavior in those problems is different as it involves large number of linear, nonlinear and non-convex type equality and inequality constraints. In this work a 57 real-world constrained optimization problems test suite is solved using two constrained metaheuristic algorithms originated from a socio-based Cohort Intelligence (CI) algorithm. The first CI-based algorithm incorporates a self-adaptive penalty function approach i.e., CI-SAPF. The second algorithm combines CI-SAPF with the intrinsic properties of the physics-based Colliding Bodies Optimization (CBO) referred to CI-SAPF-CBO. The results obtained from CI-SAPF and CI-SAPF-CBO are compared with other constrained optimization algorithms. The superiority of the proposed algorithms is discussed in details followed by future directions to evolve the constrained handling techniques.

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A second-order chain rule identity for matrix functions is proven to compute the higher-order derivatives to implement cubic-regularized Newton, and a new convergence analysis is provided for cubic-regularized Newton for matrix vector spaces. We demonstrate the applicability of our approach by conducting numerical experiments on both synthetic and real datasets. In our experiments, we formulate a new model for estimating fair and robust covariance matrices in the spirit of the Tyler's M-estimator (TME) model and demonstrate its advantage.

Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use differentiable optimal control for which the gradients of the robot's motion with respect to the parameters are required. We propose a method to efficiently compute these gradients analytically via the differential dynamic programming (DDP) algorithm using sensitivity analysis (SA). We show that we must include second-order dynamics terms when computing the gradients. However, we do not need to include them when computing the motion. We validate our approach on the pendulum and double pendulum systems. Furthermore, we compare against using the derivatives of the iterative linear quadratic regulator (iLQR), which ignores these second-order terms everywhere, on a co-design task for the Kinova arm, where we optimize the link lengths of the robot for a target reaching task. We show that optimizing using iLQR gradients diverges as ignoring the second-order dynamics affects the computation of the derivatives. Instead, optimizing using DDP gradients converges to the same optimum for a range of initial designs allowing our formulation to scale to complex systems.

As an edge intelligence algorithm for multi-device collaborative training, federated learning (FL) can reduce the communication burden but increase the computing load of wireless devices. In contrast, split learning (SL) can reduce the computing load of devices by using model splitting and assignment, but increase the communication burden to transmit intermediate results. In this paper, to exploit the advantages of FL and SL, we propose a hybrid federated split learning (HFSL) framework in wireless networks, which combines the multi-worker parallel update of FL and flexible splitting of SL. To reduce the computational idleness in model splitting, we design a parallel computing scheme for model splitting without label sharing, and theoretically analyze the influence of the delayed gradient caused by the scheme on the convergence speed. Aiming to obtain the trade-off between the training time and energy consumption, we optimize the splitting decision, the bandwidth and computing resource allocation. The optimization problem is multi-objective, and we thus propose a predictive generative adversarial network (GAN)-powered multi-objective optimization algorithm to obtain the Pareto front of the problem. Experimental results show that the proposed algorithm outperforms others in finding Pareto optimal solutions, and the solutions of the proposed HFSL dominate the solution of FL.