High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented na\"ively, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods.

Optical neural architectures (ONAs) use coding elements with optimized physical parameters to perform intelligent measurements. However, fabricating ONAs while maintaining design performances is challenging. Limitations in fabrication techniques often limit the realizable precision of the trained parameters. Physical constraints may also limit the range of values the physical parameters can hold. Thus, ONAs should be trained within the implementable constraints. However, such physics-based constraints reduce the training objective to a constrained optimization problem, making it harder to optimize with existing gradient-based methods. To alleviate these critical issues that degrade performance from simulation to realization we propose a physics-informed quantization-aware training framework. Our approach accounts for the physical constraints during the training process, leading to robust designs. We evaluate our approach on an ONA proposed in the literature, named a diffractive deep neural network (D2NN), for all-optical phase imaging and for classification of phase objects. With extensive experiments on different quantization levels and datasets, we show that our approach leads to ONA designs that are robust to quantization noise.

With the emergence of services and online applications as taxi dispatching, crowdsourcing, package or food delivery, industrials and researchers are paying attention to the online multi-task assignment optimization field to quickly and efficiently met demands. In this context, this paper is interested in the multi-task assignment problem where multiple requests (e.g. tasks) arrive over time and must be dynamically matched to (mobile) agents. This optimization problem is known to be NP-hard. In order to treat this problem with a proactive mindset, we propose to use a receding-horizon approach to determine which resources (e.g. taxis, mobile agents, drones, robots) would be available within this (possibly dynamic) receding-horizon to meet the current set of requests (i.e. tasks) as good as possible. Contrarily to several works in this domain, we have chosen to make no assumption concerning future locations of requests. To achieve fast optimized online solutions in terms of costs and amount of allocated tasks, we have designed a genetic algorithm based on a fitness function integrating the traveled distance and the age of the requests. We compared our proactive multi-task assignment with resource availability anticipation approach with a classical reactive approach. The results obtained in two benchmark problems, one synthetic and another based on real data, show that our resource availability anticipation method can achieve better results in terms of costs (e.g. traveled distance) and amount of allocated tasks than reactive approaches while decreasing resources idle time.

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning engineers with their simplicity. However, one of the weaknesses of this type of methods is the necessity to tune learning rate (step-size) for every loss function and dataset combination to solve an optimization problem and get an efficient performance in a given time budget. Stochastic Gradient Descent with Polyak Step-size (SPS) is a method that offers an update rule that alleviates the need of fine-tuning the learning rate of an optimizer. In this paper, we propose an extension of SPS that employs preconditioning techniques, such as Hutchinson's method, Adam, and AdaGrad, to improve its performance on badly scaled and/or ill-conditioned datasets.

As global attention on renewable and clean energy grows, the research and implementation of microgrids become paramount. This paper delves into the methodology of exploring the relationship between the operational and environmental costs of microgrids through multi-objective optimization models. By integrating various optimization algorithms like Genetic Algorithm, Simulated Annealing, Ant Colony Optimization, and Particle Swarm Optimization, we propose an integrated approach for microgrid optimization. Simulation results depict that these algorithms provide different dispatch results under economic and environmental dispatch, revealing distinct roles of diesel generators and micro gas turbines in microgrids. Overall, this study offers in-depth insights and practical guidance for microgrid design and operation.

Efficiently aggregating trained neural networks from local clients into a global model on a server is a widely researched topic in federated learning. Recently, motivated by diminishing privacy concerns, mitigating potential attacks, and reducing the overhead of communication, one-shot federated learning (i.e., limiting client-server communication into a single round) has gained popularity among researchers. However, the one-shot aggregation performances are sensitively affected by the non-identical training data distribution, which exhibits high statistical heterogeneity in some real-world scenarios. To address this issue, we propose a novel one-shot aggregation method with Layer-wise Posterior Aggregation, named FedLPA. FedLPA aggregates local models to obtain a more accurate global model without requiring extra auxiliary datasets or exposing any confidential local information, e.g., label distributions. To effectively capture the statistics maintained in the biased local datasets in the practical non-IID scenario, we efficiently infer the posteriors of each layer in each local model using layer-wise Laplace approximation and aggregate them to train the global parameters. Extensive experimental results demonstrate that FedLPA significantly improves learning performance over state-of-the-art methods across several metrics. Data privacy issues in Deep Learning (LeCun et al., 2015; Schmidhuber, 2015; Zhang et al., 2018; Krizhevsky et al., 2017; Amodei et al., 2016; Pouyanfar et al., 2018b;a) have grown to be a major global concern (Yang et al., 2019). To safeguard data privacy and to curb the aggregation and management of data across institutions, the distribution of data exhibits variations among clients (Yang et al., 2019). In the domain of machine learning, federated learning (FL) (McMahan et al., 2016; Kairouz et al., 2021; Li et al., 2021) has emerged as a prominent paradigm.

In this letter, we propose the use of a meta-learning based precoder optimization framework to directly optimize the Rate-Splitting Multiple Access (RSMA) precoders with partial Channel State Information at the Transmitter (CSIT). By exploiting the overfitting of the compact neural network to maximize the explicit Average Sum-Rate (ASR) expression, we effectively bypass the need for any other training data while minimizing the total running time. Numerical results reveal that the meta-learning based solution achieves similar ASR performance to conventional precoder optimization in medium-scale scenarios, and significantly outperforms sub-optimal low complexity precoder algorithms in the large-scale regime.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. A variety of self-improvement strategies are proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox. A language model can be queried to optimize virtually any objective describable in natural language. However, a program that makes multiple, structured calls to a language model can often produce outputs with higher objective values (Yao et al., 2022; 2023; Zelikman et al., 2023; Chen et al., 2022). We refer to these as "scaffolding" programs, typically written (by humans) in a programming language such as Python. Our key observation is that, for any distribution over optimization problems and any fixed language model, the design of a scaffolding program is itself an optimization problem. In this work, we introduce the Self-Taught Optimizer (STOP), a method in which code that applies a language model to improve arbitrary solutions is applied recursively to improve itself. Our approach begins with an initial seed'improver' scaffolding program that uses the language model to improve a solution to some downstream task.

Preference-based optimization algorithms are iterative procedures that seek the optimal calibration of a decision vector based only on comparisons between couples of different tunings. At each iteration, a human decision-maker expresses a preference between two calibrations (samples), highlighting which one, if any, is better than the other. The optimization procedure must use the observed preferences to find the tuning of the decision vector that is most preferred by the decision-maker, while also minimizing the number of comparisons. In this work, we formulate the preference-based optimization problem from a utility theory perspective. Then, we propose GLISp-r, an extension of a recent preference-based optimization procedure called GLISp. The latter uses a Radial Basis Function surrogate to describe the tastes of the decision-maker. Iteratively, GLISp proposes new samples to compare with the best calibration available by trading off exploitation of the surrogate model and exploration of the decision space. In GLISp-r, we propose a different criterion to use when looking for new candidate samples that is inspired by MSRS, a popular procedure in the black-box optimization framework. Compared to GLISp, GLISp-r is less likely to get stuck on local optima of the preference-based optimization problem. We motivate this claim theoretically, with a proof of global convergence, and empirically, by comparing the performances of GLISp and GLISp-r on several benchmark optimization problems.