In decision-making systems, algorithmic recourse aims to identify minimal-cost actions to alter an individual features, thereby obtaining a desired outcome. This empowers individuals to understand, question, or alter decisions that negatively affect them. However, due to the variety and sensitivity of system environments and individual personalities, quantifying the cost of a single function is nearly impossible while considering multiple criteria situations. Most current recourse mechanisms use gradient-based methods that assume cost functions are differentiable, often not applicable in real-world scenarios, resulting in sub-optimal solutions that compromise various criteria. These solutions are typically intractable and lack rigorous theoretical foundations, raising concerns regarding interpretability, reliability, and transparency from the explainable AI (XAI) perspective. To address these issues, this work proposes an algorithmic recourse framework that handles non-differentiable and discrete multi-cost functions. By formulating recourse as a multi-objective optimization problem and assigning weights to different criteria based on their importance, our method identifies Pareto optimal recourse recommendations. To demonstrate scalability, we incorporate the concept of epsilon-net, proving the ability to find approximated Pareto optimal actions. Experiments show the trade-off between different criteria and the methods scalability in large graphs. Compared to current heuristic practices, our approach provides a stronger theoretical foundation and better aligns recourse suggestions with real-world requirements.

Motivated by emerging decentralized applications, the \emph{game of coding} framework has been recently introduced to address scenarios where the adversary's control over coded symbols surpasses the fundamental limits of traditional coding theory. Still, the reward mechanism available in decentralized systems, motivates the adversary to act rationally. While the decoder, as the data collector (DC), has an acceptance and rejection mechanism, followed by an estimation module, the adversary aims to maximize its utility, as an increasing function of (1) the chance of acceptance (to increase the reward), and (2) estimation error. On the other hand, the decoder also adjusts its acceptance rule to maximize its own utility, as (1) an increasing function of the chance of acceptance (to keep the system functional), (2) decreasing function of the estimation error. Prior works within this framework rely on the assumption that the game is complete, that is, both the DC and the adversary are fully aware of each other's utility functions. However, in practice, the decoder is often unaware of the utility of the adversary. To address this limitation, we develop an algorithm enabling the DC to commit to a strategy that achieves within the vicinity of the equilibrium, without knowledge of the adversary's utility function. Our approach builds on an observation that at the equilibrium, the relationship between the probability of acceptance and the mean squared error (MSE) follows a predetermined curve independent of the specific utility functions of the players. By exploiting this invariant relationship, the DC can iteratively refine its strategy based on observable parameters, converging to a near-optimal solution. We provide theoretical guarantees on sample complexity and accuracy of the proposed scheme.

Incorporating user preferences into multi-objective Bayesian optimization (MOBO) allows for personalization of the optimization procedure. Preferences are often abstracted in the form of an unknown utility function, estimated through pairwise comparisons of potential outcomes. However, utility-driven MOBO methods can yield solutions that are dominated by nearby solutions, as non-dominance is not enforced. Additionally, classical MOBO commonly relies on estimating the entire Pareto-front to identify the Pareto-optimal solutions, which can be expensive and ignore user preferences. Here, we present a new method, termed preference-utility-balanced MOBO (PUB-MOBO), that allows users to disambiguate between near-Pareto candidate solutions. PUB-MOBO combines utility-based MOBO with local multi-gradient descent to refine user-preferred solutions to be near-Pareto-optimal. To this end, we propose a novel preference-dominated utility function that concurrently preserves user-preferences and dominance amongst candidate solutions. A key advantage of PUB-MOBO is that the local search is restricted to a (small) region of the Pareto-front directed by user preferences, alleviating the need to estimate the entire Pareto-front. PUB-MOBO is tested on three synthetic benchmark problems: DTLZ1, DTLZ2 and DH1, as well as on three real-world problems: Vehicle Safety, Conceptual Marine Design, and Car Side Impact. PUB-MOBO consistently outperforms state-of-the-art competitors in terms of proximity to the Pareto-front and utility regret across all the problems.

Semivalue-based data valuation in machine learning (ML) quantifies the contribution of individual data points to a downstream ML task by leveraging principles from cooperative game theory and the notion of utility. While this framework has been used in practice for assessing data quality, our experiments reveal inconsistent valuation outcomes across different utilities, albeit all related to ML performance. Beyond raising concerns about the reliability of data valuation, this inconsistency is challenging to interpret, as it stems from the complex interaction of the utility with data points and semivalue weights, which has barely been studied in prior work. In this paper, we take a first step toward clarifying the utility impact on semivalue-based data valuation. Specifically, we provide geometric interpretations of this impact for a broad family of classification utilities, which includes the accuracy and the arithmetic mean. We introduce the notion of spatial signatures: given a semivalue, data points can be embedded into a two-dimensional space, and utility functions map to the dual of this space. This geometric perspective separates the influence of the dataset and semivalue from that of the utility, providing a theoretical explanation for the experimentally observed sensitivity of valuation outcomes to the utility choice.

Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as SWAN (Ma et al., 2024) address this by eliminating the need for optimizer states while achieving performance comparable to Adam via a multi-step preprocessing procedure applied to instantaneous gradients. Motivated by the success of SWAN, we introduce a novel framework for designing stateless optimizers that normalizes stochastic gradients according to multiple norms. To achieve this, we propose a simple alternating scheme to enforce the normalization of gradients w.r.t these norms. We show that our procedure can produce, up to an arbitrary precision, a fixed-point of the problem, and that SWAN is a particular instance of our approach with carefully chosen norms, providing a deeper understanding of its design. However, SWAN's computationally expensive whitening/orthogonalization step limit its practicality for large LMs. Using our principled perspective, we develop of a more efficient, scalable, and practical stateless optimizer. Our algorithm relaxes the properties of SWAN, significantly reducing its computational cost while retaining its memory efficiency, making it applicable to training large-scale models. Experiments on pre-training LLaMA models with up to 1 billion parameters demonstrate a 3X speedup over Adam with significantly reduced memory requirements, outperforming other memory-efficient baselines.

We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in a given feature may affect other features. The main goal of our work is to understand \emph{when and how much agent effort is invested towards desirable features}, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them, and the information available to the agent about the classifier and the feature causal graph. In the complete information case, when agents know the classifier and the causal structure of the problem, we derive conditions ensuring that rational agents focus on features favored by the principal. We show that designing classifiers to induce desirable behavior is generally non-convex, though tractable in special cases. We also extend our analysis to settings where agents have incomplete information about the classifier or the causal graph. While optimal effort selection is again a non-convex problem under general uncertainty, we highlight special cases of partial uncertainty where this selection problem becomes tractable. Our results indicate that uncertainty drives agents to favor features with higher expected importance and lower variance, potentially misaligning with principal preferences. Finally, numerical experiments based on a cardiovascular disease risk study illustrate how to incentivize desirable modifications under uncertainty.

The memory challenges associated with training Large Language Models (LLMs) have become a critical concern, particularly when using the Adam optimizer. To address this issue, numerous memory-efficient techniques have been proposed, with GaLore standing out as a notable example designed to reduce the memory footprint of optimizer states. However, these approaches do not alleviate the memory burden imposed by activations, rendering them unsuitable for scenarios involving long context sequences or large mini-batches. Moreover, their convergence properties are still not well-understood in the literature. In this work, we introduce a Randomized Subspace Optimization framework for pre-training and fine-tuning LLMs. Our approach decomposes the high-dimensional training problem into a series of lower-dimensional subproblems. At each iteration, a random subspace is selected, and the parameters within that subspace are optimized. This structured reduction in dimensionality allows our method to simultaneously reduce memory usage for both activations and optimizer states. We establish comprehensive convergence guarantees and derive rates for various scenarios, accommodating different optimization strategies to solve the subproblems. Extensive experiments validate the superior memory and communication efficiency of our method, achieving performance comparable to GaLore and Adam.

Ensuring safe driving while maintaining travel efficiency for autonomous vehicles in dynamic and occluded environments is a critical challenge. This paper proposes an occlusion-aware contingency safety-critical planning approach for real-time autonomous driving in such environments. Leveraging reachability analysis for risk assessment, forward reachable sets of occluded phantom vehicles are computed to quantify dynamic velocity boundaries. These velocity boundaries are incorporated into a biconvex nonlinear programming (NLP) formulation, enabling simultaneous optimization of exploration and fallback trajectories within a receding horizon planning framework. To facilitate real-time optimization and ensure coordination between trajectories, we employ the consensus alternating direction method of multipliers (ADMM) to decompose the biconvex NLP problem into low-dimensional convex subproblems. The effectiveness of the proposed approach is validated through simulation studies and real-world experiments in occluded intersections. Experimental results demonstrate enhanced safety and improved travel efficiency, enabling real-time safe trajectory generation in dynamic occluded intersections under varying obstacle conditions. A video showcasing the experimental results is available at https://youtu.be/CHayG7NChqM.

Mixture-of-Experts (MoE) model architecture has emerged as a promising solution for scaling transformer models efficiently, offering sparse activation that reduces computational costs while increasing model capacity. However, as MoE models scale, they need to be distributed across GPU devices, thus face critical performance bottlenecks due to their large memory footprint. Expert parallelism distributes experts across GPUs, however, faces key challenges including an unbalanced token routing and expert activation, resulting in communication tail latency and processing inefficiencies. While existing solutions address some of these issues, they fail to resolve the dual challenges of load imbalance and communication skew. The imbalance in token processing load across experts causes uneven processing times on different GPUs, while communication skew between GPUs leads to unbalanced inter-GPU data transfers. These factors degrade the performance of MoE models by increasing tail latency and reducing overall throughput. To address these limitations, we propose an Integer Linear Programming (ILP) formulation to optimize expert placement by jointly considering token load, communication, and computation costs. We exploit the property that there is a token routing dependency across layers, where tokens routed to a specific expert in one layer are likely to be routed to a limited set of experts in the subsequent layer. Our solution, MoETuner, offers an optimal expert-to-GPU assignment that minimizes inter-GPU token routing costs and balances token processing across devices, thereby reducing tail latency and end-to-end execution time. Experimental results demonstrate 9.3% and 17.5% of end-to-end speedups for single-node and multi-node inference respectively, showcasing the potential of our ILP-based optimization for offering expert parallel solutions for next-generation MoEs.

In this work we investigate the potential of solving the discrete Optimal Transport (OT) problem with entropy regularization in a federated learning setting. Recall that the celebrated Sinkhorn algorithm transforms the classical OT linear program into strongly convex constrained optimization, facilitating first order methods for otherwise intractably large problems. A common contemporary setting that remains an open problem as far as the application of Sinkhorn is the presence of data spread across clients with distributed inter-communication, either due to clients whose privacy is a concern, or simply by necessity of processing and memory hardware limitations. In this work we investigate various natural procedures, which we refer to as Federated Sinkhorn, that handle distributed environments where data is partitioned across multiple clients. We formulate the problem as minimizing the transport cost with an entropy regularization term, subject to marginal constraints, where block components of the source and target distribution vectors are locally known to clients corresponding to each block. We consider both synchronous and asynchronous variants as well as all-to-all and server-client communication topology protocols. Each procedure allows clients to compute local operations on their data partition while periodically exchanging information with others. We provide theoretical guarantees on convergence for the different variants under different possible conditions. We empirically demonstrate the algorithms performance on synthetic datasets and a real-world financial risk assessment application. The investigation highlights the subtle tradeoffs associated with computation and communication time in different settings and how they depend on problem size and sparsity.