Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It performs comparably or favorably to AdamW but with greater memory efficiency. As we can expect from the results of a random search program, Lion incorporates elements from several existing algorithms, including signed momentum, decoupled weight decay, Polak, and Nesterov momentum, but does not fit into any existing category of theoretically grounded optimizers. Thus, even though Lion appears to perform well as a general-purpose optimizer for a wide range of tasks, its theoretical basis remains uncertain. This lack of theoretical clarity limits opportunities to further enhance and expand Lion's efficacy. This work aims to demystify Lion. Based on both continuous-time and discrete-time analysis, we demonstrate that Lion is a theoretically novel and principled approach for minimizing a general loss function $f(x)$ while enforcing a bound constraint $\|x\|_\infty \leq 1/\lambda$. Lion achieves this through the incorporation of decoupled weight decay, where $\lambda$ represents the weight decay coefficient. Our analysis is made possible by the development of a new Lyapunov function for the Lion updates. It applies to a broader family of Lion-$\kappa$ algorithms, where the $\text{sign}(\cdot)$ operator in Lion is replaced by the subgradient of a convex function $\kappa$, leading to the solution of a general composite optimization problem of $\min_x f(x) + \kappa^*(x)$. Our findings provide valuable insights into the dynamics of Lion and pave the way for further improvements and extensions of Lion-related algorithms.

Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new direction-oriented multi-objective problem by regularizing the common descent direction within a neighborhood of a direction that optimizes a linear combination of objectives such as the average loss in MTL. This formulation includes GD and MGDA as special cases, enjoys the direction-oriented benefit as in CAGrad, and facilitates the design of stochastic algorithms. To solve this problem, we propose Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad) with simple SGD type of updates, and its variant SDMGrad-OS with an efficient objective sampling in the setting where the number of objectives is large. For a constant-level regularization parameter $\lambda$, we show that SDMGrad and SDMGrad-OS provably converge to a Pareto stationary point with improved complexities and milder assumptions. For an increasing $\lambda$, this convergent point reduces to a stationary point of the linear combination of objectives. We demonstrate the superior performance of the proposed methods in a series of tasks on multi-task supervised learning and reinforcement learning. Code is provided at https://github.com/ml-opt-lab/sdmgrad.

Data-driven decision making plays an important role even in high stakes settings like medicine and public policy. Learning optimal policies from observed data requires a careful formulation of the utility function whose expected value is maximized across a population. Although researchers typically use utilities that depend on observed outcomes alone, in many settings the decision maker's utility function is more properly characterized by the joint set of potential outcomes under all actions. For example, the Hippocratic principle to "do no harm" implies that the cost of causing death to a patient who would otherwise survive without treatment is greater than the cost of forgoing life-saving treatment. We consider optimal policy learning with asymmetric counterfactual utility functions of this form that consider the joint set of potential outcomes. We show that asymmetric counterfactual utilities lead to an unidentifiable expected utility function, and so we first partially identify it. Drawing on statistical decision theory, we then derive minimax decision rules by minimizing the maximum expected utility loss relative to different alternative policies. We show that one can learn minimax loss decision rules from observed data by solving intermediate classification problems, and establish that the finite sample excess expected utility loss of this procedure is bounded by the regret of these intermediate classifiers. We apply this conceptual framework and methodology to the decision about whether or not to use right heart catheterization for patients with possible pulmonary hypertension.

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency bands. Motivated by many applications in which this differentiation is pivotal, we overcome this limitation by learning a block-sparse, frequency-dependent, partial correlation graph, in which layers correspond to different frequency bands, and partial correlations can occur over just a few layers. To this aim, we formulate and solve two nonconvex learning problems: the first has a closed-form solution and is suitable when there is prior knowledge about the number of partial correlations; the second hinges on an iterative solution based on successive convex approximation, and is effective for the general case where no prior knowledge is available. Numerical results on synthetic data show that the proposed methods outperform the current state of the art. Finally, the analysis of financial time series confirms that partial correlations exist only within a few frequency bands, underscoring how our methods enable the gaining of valuable insights that would be undetected without discriminating along the frequency domain.

Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard Combinatorial Optimization problems (CO) in the form of binary variables. Ising Hamiltonian is used to model the energy function of a system. QUBO to Ising Hamiltonian is regarded as a technique to solve various canonical optimization problems through quantum optimization algorithms. Recently, PI-GNN, a generic framework, has been proposed to address CO problems over graphs based on Graph Neural Network (GNN) architecture. They introduced a generic QUBO-formulated Hamiltonian-inspired loss function that was directly optimized using GNN. PI-GNN is highly scalable but there lies a noticeable decrease in the number of satisfied constraints when compared to problem-specific algorithms and becomes more pronounced with increased graph densities. Here, We identify a behavioral pattern related to it and devise strategies to improve its performance. Another group of literature uses Reinforcement learning (RL) to solve the aforementioned NP-hard problems using problem-specific reward functions. In this work, we also focus on creating a bridge between the RL-based solutions and the QUBO-formulated Hamiltonian. We formulate and empirically evaluate the compatibility of the QUBO-formulated Hamiltonian as the generic reward function in the RL-based paradigm in the form of rewards. Furthermore, we also introduce a novel Monty Carlo Tree Search-based strategy with GNN where we apply a guided search through manual perturbation of node labels during training. We empirically evaluated our methods and observed up to 44% improvement in the number of constraint violations compared to the PI-GNN.

This paper addresses aircraft delays, emphasizing their impact on safety and financial losses. To mitigate these issues, an innovative machine learning (ML)-enhanced landing scheduling methodology is proposed, aiming to improve automation and safety. Analyzing flight arrival delay scenarios reveals strong multimodal distributions and clusters in arrival flight time durations. A multi-stage conditional ML predictor enhances separation time prediction based on flight events. ML predictions are then integrated as safety constraints in a time-constrained traveling salesman problem formulation, solved using mixed-integer linear programming (MILP). Historical flight recordings and model predictions address uncertainties between successive flights, ensuring reliability. The proposed method is validated using real-world data from the Atlanta Air Route Traffic Control Center (ARTCC ZTL). Case studies demonstrate an average 17.2% reduction in total landing time compared to the First-Come-First-Served (FCFS) rule. Unlike FCFS, the proposed methodology considers uncertainties, instilling confidence in scheduling. The study concludes with remarks and outlines future research directions.

The high simulation cost has been a bottleneck of practical analog/mixed-signal design automation. Many learning-based algorithms require thousands of simulated data points, which is impractical for expensive to simulate circuits. We propose a learning-based algorithm that can be trained using a small amount of data and, therefore, scalable to tasks with expensive simulations. Our efficient algorithm solves the post-layout performance optimization problem where simulations are known to be expensive. Our comprehensive study also solves the schematic-level sizing problem. For efficient optimization, we utilize Bayesian Neural Networks as a regression model to approximate circuit performance. For layout-aware optimization, we handle the problem as a multi-fidelity optimization problem and improve efficiency by exploiting the correlations from cheaper evaluations. We present three test cases to demonstrate the efficiency of our algorithms. Our tests prove that the proposed approach is more efficient than conventional baselines and state-of-the-art algorithms.

Federated learning is a machine learning protocol that enables a large population of agents to collaborate over multiple rounds to produce a single consensus model. There are several federated learning applications where agents may choose to defect permanently$-$essentially withdrawing from the collaboration$-$if they are content with their instantaneous model in that round. This work demonstrates the detrimental impact of such defections on the final model's robustness and ability to generalize. We also show that current federated optimization algorithms fail to disincentivize these harmful defections. We introduce a novel optimization algorithm with theoretical guarantees to prevent defections while ensuring asymptotic convergence to an effective solution for all participating agents. We also provide numerical experiments to corroborate our findings and demonstrate the effectiveness of our algorithm.

We introduce a novel optimization problem formulation that departs from the conventional way of minimizing machine learning model loss as a black-box function. Unlike traditional formulations, the proposed approach explicitly incorporates an initially pre-trained model and random sketch operators, allowing for sparsification of both the model and gradient during training. We establish insightful properties of the proposed objective function and highlight its connections to the standard formulation. Furthermore, we present several variants of the Stochastic Gradient Descent (SGD) method adapted to the new problem formulation, including SGD with general sampling, a distributed version, and SGD with variance reduction techniques. We achieve tighter convergence rates and relax assumptions, bridging the gap between theoretical principles and practical applications, covering several important techniques such as Dropout and Sparse training. This work presents promising opportunities to enhance the theoretical understanding of model training through a sparsification-aware optimization approach.

Quantum state preparation, a crucial subroutine in quantum computing, involves generating a target quantum state from initialized qubits. Arbitrary state preparation algorithms can be broadly categorized into arithmetic decomposition (AD) and variational quantum state preparation (VQSP). AD employs a predefined procedure to decompose the target state into a series of gates, whereas VQSP iteratively tunes ansatz parameters to approximate target state. VQSP is particularly apt for Noisy-Intermediate Scale Quantum (NISQ) machines due to its shorter circuits. However, achieving noise-robust parameter optimization still remains challenging. We present RobustState, a novel VQSP training methodology that combines high robustness with high training efficiency. The core idea involves utilizing measurement outcomes from real machines to perform back-propagation through classical simulators, thus incorporating real quantum noise into gradient calculations. RobustState serves as a versatile, plug-and-play technique applicable for training parameters from scratch or fine-tuning existing parameters to enhance fidelity on target machines. It is adaptable to various ansatzes at both gate and pulse levels and can even benefit other variational algorithms, such as variational unitary synthesis. Comprehensive evaluation of RobustState on state preparation tasks for 4 distinct quantum algorithms using 10 real quantum machines demonstrates a coherent error reduction of up to 7.1 $\times$ and state fidelity improvement of up to 96\% and 81\% for 4-Q and 5-Q states, respectively. On average, RobustState improves fidelity by 50\% and 72\% for 4-Q and 5-Q states compared to baseline approaches.