Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple formula that can find the right allocation for every individual. As a result, investors may use different asset allocations' strategy to try to fulfil their financial objectives. In this work, we conduct an extensive benchmark study to determine the efficacy and reliability of a number of optimization techniques. In particular, we focus on traditional approaches based on Modern Portfolio Theory, and on machine-learning approaches based on deep reinforcement learning. We assess the model's performance under different market tendency, i.e., both bullish and bearish markets. For reproducibility, we provide the code implementation code in this repository.

Deep decarbonization of the energy sector will require massive penetration of stochastic renewable energy resources and an enormous amount of grid asset coordination; this represents a challenging paradigm for the power system operators who are tasked with maintaining grid stability and security in the face of such changes. With its ability to learn from complex datasets and provide predictive solutions on fast timescales, machine learning (ML) is well-posed to help overcome these challenges as power systems transform in the coming decades. In this work, we outline five key challenges (dataset generation, data pre-processing, model training, model assessment, and model embedding) associated with building trustworthy ML models which learn from physics-based simulation data. We then demonstrate how linking together individual modules, each of which overcomes a respective challenge, at sequential stages in the machine learning pipeline can help enhance the overall performance of the training process. In particular, we implement methods that connect different elements of the learning pipeline through feedback, thus "closing the loop" between model training, performance assessments, and re-training. We demonstrate the effectiveness of this framework, its constituent modules, and its feedback connections by learning the N-1 small-signal stability margin associated with a detailed model of a proposed North Sea Wind Power Hub system.

This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program, through the use of neural networks. We encode the feasible space of optimization problems characterized by both tractable and intractable constraints, e.g. differential equations, to a neural network. Leveraging an exact mixed-integer reformulation of neural networks, we solve mixed-integer linear programs that accurately approximate solutions to the originally intractable non-linear optimization problem. We apply our methods to the AC optimal power flow problem (AC-OPF), where directly including dynamic security constraints renders the AC-OPF intractable. Our proposed approach has the potential to be significantly more scalable than traditional approaches. We demonstrate our approach for power system operation considering N-1 security and small-signal stability, showing how it can efficiently obtain cost-optimal solutions which at the same time satisfy both static and dynamic security constraints.

The federated learning (FL) framework enables edge clients to collaboratively learn a shared inference model while keeping privacy of training data on clients. Recently, many heuristics efforts have been made to generalize centralized adaptive optimization methods, such as SGDM, Adam, AdaGrad, etc., to federated settings for improving convergence and accuracy. However, there is still a paucity of theoretical principles on where to and how to design and utilize adaptive optimization methods in federated settings. This work aims to develop novel adaptive optimization methods for FL from the perspective of dynamics of ordinary differential equations (ODEs). First, an analytic framework is established to build a connection between federated optimization methods and decompositions of ODEs of corresponding centralized optimizers. Second, based on this analytic framework, a momentum decoupling adaptive optimization method, FedDA, is developed to fully utilize the global momentum on each local iteration and accelerate the training convergence. Last but not least, full batch gradients are utilized to mimic centralized optimization in the end of the training process to ensure the convergence and overcome the possible inconsistency caused by adaptive optimization methods.

We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only the distance measurements to a few 'landmark nodes'. This landmark heuristic makes L-hydra applicable to large-scale graphs and improves upon previously introduced methods. As a mathematical justification, we show that a point configuration in d-dimensional hyperbolic space can be perfectly recovered (up to isometry) from distance measurements to just d+1 landmarks. We also show that L-hydra solves a two-stage strain-minimization problem, similar to our previous (unlandmarked) method 'hydra'. Testing on real network data, we show that L-hydra is an order of magnitude faster than existing hyperbolic embedding methods and scales linearly in the number of nodes. While the embedding error of L-hydra is higher than the error of existing methods, we introduce an extension, L-hydra+, which outperforms existing methods in both runtime and embedding quality.

Microstructures, i.e., architected materials, are designed today, typically, by maximizing an objective, such as bulk modulus, subject to a volume constraint. However, in many applications, it is often more appropriate to impose constraints on other physical quantities of interest. In this paper, we consider such generalized microstructural optimization problems where any of the microstructural quantities, namely, bulk, shear, Poisson ratio, or volume, can serve as the objective, while the remaining can serve as constraints. In particular, we propose here a neural-network (NN) framework to solve such problems. The framework relies on the classic density formulation of microstructural optimization, but the density field is represented through the NN's weights and biases. The main characteristics of the proposed NN framework are: (1) it supports automatic differentiation, eliminating the need for manual sensitivity derivations, (2) smoothing filters are not required due to implicit filtering, (3) the framework can be easily extended to multiple-materials, and (4) a high-resolution microstructural topology can be recovered through a simple post-processing step. The framework is illustrated through a variety of microstructural optimization problems.

Online trajectory planners enable quadrotors to safely and smoothly navigate in unknown cluttered environments. However, tuning parameters is challenging since modern planners have become too complex to mathematically model and predict their interaction with unstructured environments. This work takes humans out of the loop by proposing a planner parameter adaptation framework that formulates objectives into two complementary categories and optimizes them asynchronously. Objectives evaluated with and without trajectory execution are optimized using Bayesian Optimization (BayesOpt) and Particle Swarm Optimization (PSO), respectively. By combining two kinds of objectives, the total convergence rate of the black-box optimization is accelerated while the dimension of optimized parameters can be increased. Benchmark comparisons demonstrate its superior performance over other strategies. Tests with changing obstacle densities validate its real-time environment adaption, which is difficult for prior manual tuning. Real-world flights with different drone platforms, environments, and planners show the proposed framework's scalability and effectiveness.

Variational quantum algorithms such as the Quantum Approximation Optimization Algorithm (QAOA) in recent years have gained popularity as they provide the hope of using NISQ devices to tackle hard combinatorial optimization problems. It is, however, known that at low depth, certain locality constraints of QAOA limit its performance. To go beyond these limitations, a non-local variant of QAOA, namely recursive QAOA (RQAOA), was proposed to improve the quality of approximate solutions. The RQAOA has been studied comparatively less than QAOA, and it is less understood, for instance, for what family of instances it may fail to provide high quality solutions. However, as we are tackling $\mathsf{NP}$-hard problems (specifically, the Ising spin model), it is expected that RQAOA does fail, raising the question of designing even better quantum algorithms for combinatorial optimization. In this spirit, we identify and analyze cases where RQAOA fails and, based on this, propose a reinforcement learning enhanced RQAOA variant (RL-RQAOA) that improves upon RQAOA. We show that the performance of RL-RQAOA improves over RQAOA: RL-RQAOA is strictly better on these identified instances where RQAOA underperforms, and is similarly performing on instances where RQAOA is near-optimal. Our work exemplifies the potentially beneficial synergy between reinforcement learning and quantum (inspired) optimization in the design of new, even better heuristics for hard problems.

Clustering is a representative unsupervised method widely applied in multi-modal and multi-view scenarios. Multiple kernel clustering (MKC) aims to group data by integrating complementary information from base kernels. As a representative, late fusion MKC first decomposes the kernels into orthogonal partition matrices, then learns a consensus one from them, achieving promising performance recently. However, these methods fail to consider the noise inside the partition matrix, preventing further improvement of clustering performance. We discover that the noise can be disassembled into separable dual parts, i.e. N-noise and C-noise (Null space noise and Column space noise). In this paper, we rigorously define dual noise and propose a novel parameter-free MKC algorithm by minimizing them. To solve the resultant optimization problem, we design an efficient two-step iterative strategy. To our best knowledge, it is the first time to investigate dual noise within the partition in the kernel space. We observe that dual noise will pollute the block diagonal structures and incur the degeneration of clustering performance, and C-noise exhibits stronger destruction than N-noise. Owing to our efficient mechanism to minimize dual noise, the proposed algorithm surpasses the recent methods by large margins.

We present the implementation of nonlinear control algorithms based on linear and quadratic approximations of the objective from a functional viewpoint. We present a gradient descent, a Gauss-Newton method, a Newton method, differential dynamic programming approaches with linear quadratic or quadratic approximations, various line-search strategies, and regularized variants of these algorithms. We derive the computational complexities of all algorithms in a differentiable programming framework and present sufficient optimality conditions. We compare the algorithms on several benchmarks, such as autonomous car racing using a bicycle model of a car. The algorithms are coded in a differentiable programming language in a publicly available package.