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Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization

2026-09-21T12:20:42Z

Title: Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization Authors: Jadav, Hareshkumar; Singh, Ranveer Abstract: We study the maximization of nonnegative, non-monotone γ-weakly diminishing returns (DR) submodular functions over down-closed convex bodies. The weakly DR model relaxes classical diminishing returns by allowing marginal gains to decay up to a multiplicative factor γ ∈ (0, 1], capturing a broad class of objectives that interpolate between monotone and fully non-monotone DR submodularity. Existing methods in this regime achieve guarantees that deteriorate rapidly as γ decreases and fail to recover the best known bounds in the fully DR case. We develop a γ-aware algorithmic framework that combines a Frank-Wolfe guided measured continuous greedy procedure with a γ-weighted double-greedy method. Our analysis explicitly accounts for the asymmetric structure induced by weak diminishing returns, yielding γ-dependent progress certificates that remain valid across the entire weakly DR spectrum. As a result, we obtain an approximation guarantee that strictly improves upon the baseline γe−γ for all γ ∈ (0, 1) and recovers the current best constant 0.401 when γ = 1. The proposed algorithms are projection free, use only first order information and linear optimization oracles, and run in polynomial time. © 2026, Transactions on Machine Learning Research. All rights reserved.

Fault-Aware RUL Prediction for Diesel Engines Using Physics-Motivated Degradation Models

2026-08-07T12:27:04Z

Title: Fault-Aware RUL Prediction for Diesel Engines Using Physics-Motivated Degradation Models Authors: Panchal, Pratham Abstract: Remaining Useful Life (RUL) prediction is a key problem in Prognostics and Health Management for diesel engines operating under diverse fault conditions. Although data driven models such as Long Short Term Memory (LSTM) networks have shown strong predictive capability, their performance differs greatly depending on the type of fault. This paper investigates influence of fault specific degradation physics on RUL predictability. This is achieved by modelling six common diesel engine faults using physics motivated degradation formulations and synthetic run-to-failure datasets. This work involves training separate LSTM models for each fault. Separate LSTM models has been trained for each fault under a strictly leakage-free evaluation protocol. The paper further demonstrates that attainable RUL accuracy is governed primarily by degradation time scale and signal observability rather than model architecture alone. The proposed framework is intended for controlled comparative analysis rather than direct field deployment, and it highlights the need for fault-aware evaluation in data-driven prognostics. © 2026 IEEE.

Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization

2026-07-09T06:48:13Z

Title: Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization Authors: Jadav, Hareshkumar; Singh, Ranveer Abstract: Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone γ-weakly DR-submodular function over a down-closed convex body. Our main result is an approximation algorithm whose guarantee depends smoothly on γ; in particular, when γ = 1 (the DR-submodular case) our bound recovers the 0.401 approximation factor, while for γ < 1 the guarantee degrades gracefully and, it improves upon previously reported bounds for γ-weakly DR-submodular maximization under the same constraints. Our approach combines a Frank-Wolfe-guided continuous-greedy framework with a γ-aware double-greedy step, yielding a simple yet effective procedure for handling non-monotonicity. This results in state-of-the-art guarantees for non-monotone γ-weakly DR-submodular maximization over down-closed convex bodies. © 2026 International Foundation for Autonomous Agents and Multiagent Systems.