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Ermin Wei

Publications and source records attributed to Ermin Wei.

At least 19 recordsLinked to original sources

In-Context Reward Adaptation for Robust Preference Modeling

Reinforcement Learning from Human Feedback (RLHF) typically relies on static reward models to align Large Language Models with human preferences. However, human values are inherently diverse and heterogeneous, and a single reward model often lacks the robustness required to generalize to unseen preference domains. While existing multi-reward frameworks attempt to address this, they are often restricted to a fixed set of known domains and fail to adapt to unseen human distributions without costly retraining. In this work, we propose In-Context Reward Adaptation, a transformer-based framework designed to model diverse and unseen human preferences on the fly. By leveraging the in-context learning capabilities of transformers, our approach adaptively infers the underlying reward structure from a small set of preference demonstrations. We demonstrate that while a standard transformer architecture is insufficient for this task by characterizing an asymptotic bias to the ground-truth, incorporating human response time as an auxiliary input signal enables the model to successfully adapt to preferences from previously unseen domains. Our findings show that this approach provides a more robust foundation for preference modeling, allowing for the representation of heterogeneous rewards and preference distribution shift, and offering a scalable path toward more flexible human-AI alignment.

cs.LG

P-dit Probabilistic Ising Machine for Solving the Quadratic Assignment Problem

Combinatorial optimization problems represent a wide range of real-world scenarios where complicated interactions make it difficult to find the best solution. One example is the quadratic assignment problem (QAP), which involves determining the optimal placement of facilities at set locations which minimizes the products of material flow and facility distance. This representation is descriptive of many real-world scenarios, including the aggregate transportation costs of a supply chain. In this work, a probabilistic Ising machine (PIM) approach is implemented using probabilistic d-dimensional variables (p-dits), which are generalized, multi-state and multi-dimensional extensions to probabilistic bits (p-bits). Each p-dit corresponds to a location and stochastically oscillates between facility assignments based on the influence of the other p-dits. We show that with the same runtime and CPU, the PIM finds the best-known solution on 95% of considered instances from the QAP Library dataset, compared to just 36% for the standard Gurobi solver. For the unique largest problem in the library, a 2 to 3 order-of-magnitude decrease is observed in the time needed to reach specific solution qualities. We also show parallelization of our PIM through GPU implementations. A comparison to state-of-the-art QAP solver algorithms shows that they are consistently outperformed by both CPU and GPU implementations of the p-dit Ising machine.

physics.app-ph

Routing Equilibrium in Mixed-Autonomy Traffic Networks with Altruistic Autonomous Agents

Recent advancements in vehicle autonomy have drawn interest in understanding the impact of autonomous vehicles on traffic systems. In this paper, we study a traffic assignment problem in a mixed-autonomy setting where both human-driven and autonomous vehicles coexist. We model the interaction as a simultaneous routing game where human drivers are self-interested and aim to minimize their own travel times, while autonomous agents are altruistic and aim to minimize the total social cost. The standard nonatomic congestion game analysis establishes the existence of equilibrium to this game under convex cost functions, and does not have any implication of its uniqueness. In this work, we formulate the equilibrium as a variational inequality (VI), which enables us to establish the equilibrium existence without convexity assumption, and guarantees the uniqueness of the aggregated link flow and social cost at equilibrium under a specific class of cost functions. Leveraging this VI framework, we provide sufficient conditions under which including autonomous agents improves, deteriorates, or has no effect on social cost. While the possibility of deterioration has been established in prior work, our results complement existing worst-case bounds by explicitly characterizing sufficient conditions under which each outcome occurs, thereby providing a deeper understanding of mixed-autonomy traffic systems. Furthermore, we consider a centralized scenario where a social planner optimizes the routing of autonomous agents, and show that the same equilibrium is achieved as in the decentralized scenario when assuming convex costs.Finally, we conduct numerical experiments that illustrate how social cost changes with the amount of autonomous vehicles under different system parameters.

cs.GT

Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning -- most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization -- and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a \emph{spike-and-flat} shape -- a few dominant eigenvalues followed by an approximately uniform tail -- across layers and training stages, holding exactly under a rank-$\rho$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

cs.LG

Policy Gradient Primal-Dual Method for Safe Reinforcement Learning from Human Feedback

Safe Reinforcement Learning from Human Feedback (Safe RLHF) has recently achieved empirical success in developing helpful and harmless large language models by decoupling human preferences regarding helpfulness and harmlessness. Existing approaches typically rely on fitting fixed horizon reward models from human feedback and have only been validated empirically. In this paper, we formulate safe RLHF as an infinite horizon discounted Con- strained Markov Decision Process (CMDP), since humans may interact with the model over a continuing sequence of interactions rather than within a single finite episode. We propose two Safe RLHF algorithms that do not require reward model fitting and, in contrast to prior work assuming fixed-length trajectories, support flexible trajectory lengths for training. Both algo- rithms are based on the primal-dual method and achieve global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries. To the best of our knowledge, this is the first work to study infinite horizon discounted CMDP under human feedback and establish global, non-asymptotic convergence.

cs.LG

Distributed Edge Computing Task Allocation with Network Effects

Field-deployable edge computing nodes form a network and are used to complete scientific tasks for remote sensing and monitoring. The networked nodes collectively decide which scientific applications to run while they are constrained by various factors, such as differing hardware constraints from heterogeneous nodes and time-varying quality of service (QoS) requirements. We model the problem of task allocation as an optimization problem that maximizes the QoS, subject to the constraints. We solve the optimization problem using a dual-descent method, which can be easily implemented in a distributed way subject to the communication constraints of the network. Using a simulation that uses real-world data collected from Sage, a distributed sensor network, we analyze our policy's performance in dynamic situations where the required QoS and the nodes' capabilities change, and verify that it can adapt and return a feasible solution while accounting for those changes.

math.OC

Optimal Battery Placement in Power Grid

We study the optimal placement of an unlimited-capacity battery in power grids under a centralized market model, where the independent system operator (ISO) aims to minimize total generation costs through load shifting. The optimal battery placement is not well understood by the existing literature, especially regarding the influence of network topology on minimizing generation costs. Our work starts with decomposing the Mixed-Integer Linear Programming (MILP) problem into a series of Linear Programming (LP) formulations. For power grids with sufficiently large generation capacity or tree topologies, we derive analytical cost expressions demonstrating that, under reasonable assumptions, the weighted degree is the only topological factor for optimal battery placement. We also discuss the minor impact of higher-order topological conditions on tree-topology networks. To find the localized nature of a single battery's impact, we establish that the relative cost-saving benefit of a single battery decreases as the network scales. Furthermore, we design a low-complexity algorithm for weakly-cyclic networks. Numerical experiments show that our algorithm is not only approximately 100 times faster than commercial solvers but also maintains high accuracy even when some theoretical assumptions are relaxed.

eess.SY

Extended-variable probabilistic computing with p-dits

Ising machines can solve combinatorial optimization problems by representing them as energy minimization problems. A common implementation is the probabilistic Ising machine (PIM), which uses probabilistic (p-) bits to represent coupled binary spins. However, many real-world problems have complex data representations that do not map naturally into a binary encoding, leading to a significant increase in hardware resources and time-to-solution. Here, we describe a generalized spin model that supports an arbitrary number of spin dimensions, each with an arbitrary real component. We define the probabilistic d-dimensional bit (p-dit) as the base unit of a p-computing implementation of this model. We further describe two restricted forms of p-dits for specific classes of common problems and implement them experimentally on an application-specific integrated circuit (ASIC): (A) isotropic p-dits, which simplify the implementation of categorical variables resulting in ~34x performance improvement compared to a p-bit implementation on an example 3-partition problem. (B) Probabilistic integers (p-ints), which simplify the representation of numeric values and provide ~5x improvement compared to a p-bit implementation of an example integer linear programming (ILP) problem. Additionally, we report a field-programmable gate array (FPGA) p-int-based integer quadratic programming (IQP) solver which shows ~64x faster time-to-solution compared to the best of a series of state-of-the-art software solvers. The generalized formulation of probabilistic variables presented here provides a path to solving large-scale optimization problems on various hardware platforms including digital CMOS.

physics.app-ph

Incentive Analysis for Agent Participation in Federated Learning

Federated learning offers a decentralized approach to machine learning, where multiple agents collaboratively train a model while preserving data privacy. In this paper, we investigate the decision-making and equilibrium behavior in federated learning systems, where agents choose between participating in global training or conducting independent local training. The problem is first modeled as a stage game and then extended to a repeated game to analyze the long-term dynamics of agent participation. For the stage game, we characterize the participation patterns and identify Nash equilibrium, revealing how data heterogeneity influences the equilibrium behavior-specifically, agents with similar data qualities will participate in FL as a group. We also derive the optimal social welfare and show that it coincides with Nash equilibrium under mild assumptions. In the repeated game, we propose a privacy-preserving, computationally efficient myopic strategy. This strategy enables agents to make practical decisions under bounded rationality and converges to a neighborhood of Nash equilibrium of the stage game in finite time. By combining theoretical insights with practical strategy design, this work provides a realistic and effective framework for guiding and analyzing agent behaviors in federated learning systems.

cs.GT

A Decomposition Framework for Nonlinear Nonconvex Two-Stage Optimization

We propose a new decomposition framework for continuous nonlinear constrained two-stage optimization, where both first- and second-stage problems can be nonconvex. A smoothing technique based on an interior-point formulation renders the optimal solution of the second-stage problem differentiable with respect to the first-stage parameters. As a consequence, efficient off-the-shelf optimization packages can be utilized. We show that the solution of the nonconvex second-stage problem behaves locally like a differentiable function so that existing proofs can be applied to prove the convergence of the iterates to first-order optimal points for the first-stage. We also prove fast local convergence of the algorithm as the barrier parameter is driven to zero. Numerical experiments for large-scale instances demonstrate the computational advantages of the decomposition framework.

math.OC

Debiasing Federated Learning with Correlated Client Participation

In cross-device federated learning (FL) with millions of mobile clients, only a small subset of clients participate in training in every communication round, and Federated Averaging (FedAvg) is the most popular algorithm in practice. Existing analyses of FedAvg usually assume the participating clients are independently sampled in each round from a uniform distribution, which does not reflect real-world scenarios. This paper introduces a theoretical framework that models client participation in FL as a Markov chain to study optimization convergence when clients have non-uniform and correlated participation across rounds. We apply this framework to analyze a more general and practical pattern: every client must wait a minimum number of $R$ rounds (minimum separation) before re-participating. We theoretically prove and empirically observe that increasing minimum separation reduces the bias induced by intrinsic non-uniformity of client availability in cross-device FL systems. Furthermore, we develop an effective debiasing algorithm for FedAvg that provably converges to the unbiased optimal solution under arbitrary minimum separation and unknown client availability distribution.

cs.LG

Exact Label Recovery in Euclidean Random Graphs

In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label. Our goal is to infer the vertex labels, given edge weights whose distributions depend on the vertex labels as well as their geometric positions. Our general model provides a geometric extension of popular graph and matrix problems, including submatrix localization and $\mathbb{Z}_2$-synchronization, and includes the Geometric Stochastic Block Model (proposed by Sankararaman and Baccelli) as a special case. We study the fundamental limits of exact recovery of the vertex labels. Under a mild distinctness of distributions assumption, we determine the information-theoretic threshold for exact label recovery, in terms of a Chernoff-Hellinger divergence criterion. Impossibility of recovery below the threshold is proven by a unified analysis using a Cram\'er lower bound. Achievability above the threshold is proven via an efficient two-phase algorithm, where the first phase computes an almost-exact labeling through a local propagation scheme, while the second phase refines the labels. The information-theoretic threshold is dictated by the performance of the so-called genie estimator, which decodes the label of a single vertex given all the other labels. This shows that our proposed models exhibit the local-to-global amplification phenomenon.

cs.SI

On the Effect of Bounded Rationality in Electricity Markets

Nash equilibrium is a common solution concept that captures strategic interaction in electricity market analysis. However, it requires a fundamental but impractical assumption that all market participants are fully rational, implying unlimited computational resources and cognitive abilities. To tackle the limitation, level-k reasoning is proposed and studied to model the bounded rational behaviors. In this paper, we consider a Cournot competition in electricity markets with two suppliers, both following level-k reasoning. One is a self-interested firm and the other serves as a benevolent social planner. First, we observe that the optimal strategy of the social planner corresponds to a particular rationality level, where being either less or more rational may both result in reduced social welfare. We then investigate the effect of bounded rationality on social welfare performance and find that it can largely deviate from that at the Nash equilibrium point. From the perspective of the social planner, we characterize optimal, expectation maximizing and robust maximin strategies, when having access to different information. Finally, by designing its utility function, we find that social welfare is better off if the social planner cooperates with or fights the self-interested firm. Numerical experiments further demonstrate and validate our findings.

cs.GT

Hessian-Free Online Certified Unlearning

Machine unlearning strives to uphold the data owners' right to be forgotten by enabling models to selectively forget specific data. Recent advances suggest pre-computing and storing statistics extracted from second-order information and implementing unlearning through Newton-style updates. However, the Hessian matrix operations are extremely costly and previous works conduct unlearning for empirical risk minimizer with the convexity assumption, precluding their applicability to high-dimensional over-parameterized models and the nonconvergence condition. In this paper, we propose an efficient Hessian-free unlearning approach. The key idea is to maintain a statistical vector for each training data, computed through affine stochastic recursion of the difference between the retrained and learned models. We prove that our proposed method outperforms the state-of-the-art methods in terms of the unlearning and generalization guarantees, the deletion capacity, and the time/storage complexity, under the same regularity conditions. Through the strategy of recollecting statistics for removing data, we develop an online unlearning algorithm that achieves near-instantaneous data removal, as it requires only vector addition. Experiments demonstrate that our proposed scheme surpasses existing results by orders of magnitude in terms of time/storage costs with millisecond-level unlearning execution, while also enhancing test accuracy.

cs.LG

A Stochastic Quasi-Newton Method for Non-convex Optimization with Non-uniform Smoothness

Classical convergence analyses for optimization algorithms rely on the widely-adopted uniform smoothness assumption. However, recent experimental studies have demonstrated that many machine learning problems exhibit non-uniform smoothness, meaning the smoothness factor is a function of the model parameter instead of a universal constant. In particular, it has been observed that the smoothness grows with respect to the gradient norm along the training trajectory. Motivated by this phenomenon, the recently introduced $(L_0, L_1)$-smoothness is a more general notion, compared to traditional $L$-smoothness, that captures such positive relationship between smoothness and gradient norm. Under this type of non-uniform smoothness, existing literature has designed stochastic first-order algorithms by utilizing gradient clipping techniques to obtain the optimal $\mathcal{O}(\epsilon^{-3})$ sample complexity for finding an $\epsilon$-approximate first-order stationary solution. Nevertheless, the studies of quasi-Newton methods are still lacking. Considering higher accuracy and more robustness for quasi-Newton methods, in this paper we propose a fast stochastic quasi-Newton method when there exists non-uniformity in smoothness. Leveraging gradient clipping and variance reduction, our algorithm can achieve the best-known $\mathcal{O}(\epsilon^{-3})$ sample complexity and enjoys convergence speedup with simple hyperparameter tuning. Our numerical experiments show that our proposed algorithm outperforms the state-of-the-art approaches.

cs.LG

Strategic Data Revocation in Federated Unlearning

By allowing users to erase their data's impact on federated learning models, federated unlearning protects users' right to be forgotten and data privacy. Despite a burgeoning body of research on federated unlearning's technical feasibility, there is a paucity of literature investigating the considerations behind users' requests for data revocation. This paper proposes a non-cooperative game framework to study users' data revocation strategies in federated unlearning. We prove the existence of a Nash equilibrium. However, users' best response strategies are coupled via model performance and unlearning costs, which makes the equilibrium computation challenging. We obtain the Nash equilibrium by establishing its equivalence with a much simpler auxiliary optimization problem. We also summarize users' multi-dimensional attributes into a single-dimensional metric and derive the closed-form characterization of an equilibrium, when users' unlearning costs are negligible. Moreover, we compare the cases of allowing and forbidding partial data revocation in federated unlearning. Interestingly, the results reveal that allowing partial revocation does not necessarily increase users' data contributions or payoffs due to the game structure. Additionally, we demonstrate that positive externalities may exist between users' data revocation decisions when users incur unlearning costs, while this is not the case when their unlearning costs are negligible.

cs.GT

Incentivized Federated Learning and Unlearning

To protect users' right to be forgotten in federated learning, federated unlearning aims at eliminating the impact of leaving users' data on the global learned model. The current research in federated unlearning mainly concentrated on developing effective and efficient unlearning techniques. However, the issue of incentivizing valuable users to remain engaged and preventing their data from being unlearned is still under-explored, yet important to the unlearned model performance. This paper focuses on the incentive issue and develops an incentive mechanism for federated learning and unlearning. We first characterize the leaving users' impact on the global model accuracy and the required communication rounds for unlearning. Building on these results, we propose a four-stage game to capture the interaction and information updates during the learning and unlearning process. A key contribution is to summarize users' multi-dimensional private information into one-dimensional metrics to guide the incentive design. We further investigate whether allowing federated unlearning is beneficial to the server and users, compared to a scenario without unlearning. Interestingly, users usually have a larger total payoff in the scenario with higher costs, due to the server's excess incentives under information asymmetry. The numerical results demonstrate the necessity of unlearning incentives for retaining valuable leaving users, and also show that our proposed mechanisms decrease the server's cost by up to 53.91\% compared to state-of-the-art benchmarks.

cs.GT

Supply Function Equilibrium in Networked Electricity Markets

We study deregulated power markets with strategic power suppliers. In deregulated markets, each supplier submits its supply function (i.e., the amount of electricity it is willing to produce at various prices) to the independent system operator (ISO), who based on the submitted supply functions, dispatches the suppliers to clear the market with minimal total generation cost. If all suppliers reported their true marginal cost functions as supply functions, the market outcome would be efficient (i.e., the total generation cost is minimized). However, when suppliers are strategic and aim to maximize their own profits, the reported supply functions are not necessarily the true marginal cost functions, and the resulting market outcome may be inefficient. The efficiency loss depends crucially on the topology of the underlying transmission network. This paper provides an analytical upper bound of the efficiency loss due to strategic suppliers, and proves that the bound is tight under a large class of transmission networks (i.e., weakly cyclic networks). Our upper bound sheds light on how the efficiency loss depends on the transmission network topology (e.g., the degrees of nodes, the admittances and flow limits of transmission lines).

cs.GT