Lagrangian approach, which involves adding a regularization term to the loss function.

Lagrangian approach, which involves adding a regularization term to the loss function.

Recent efforts to develop trustworthy AI systems with accountability guarantees have led to widespread use of machine learning formulations incorporating external requirements, or constraints. These requirements are often enforced via penalization--adding fixed-weight terms to the task loss. We argue this approach is fundamentally ill-suited since there may be no penalty coefficient that simultaneously ensures constraint satisfaction and optimal constrained performance, i.e., that truly solves the constrained problem. Moreover, tuning these coefficients requires costly trial-and-error, incurring significant time and computational overhead. We, therefore, advocate for broader adoption of tailored constrained optimization methods--such as the Lagrangian approach, which jointly optimizes the penalization "coefficients" (the Lagrange multipliers) and the model parameters. Such methods (i) truly solve the constrained problem and do so accountably, by clearly defining feasibility and verifying when it is achieved, (ii) eliminate the need for extensive penalty tuning, and (iii) integrate seamlessly with modern deep learning pipelines.

The persistent challenge of bias in machine learning models necessitates robust solutions to ensure parity and equal treatment across diverse groups, particularly in classification tasks. Current methods for mitigating bias often result in information loss and an inadequate balance between accuracy and fairness. To address this, we propose a novel methodology grounded in bilevel optimization principles. Our deep learning-based approach concurrently optimizes for both accuracy and fairness objectives, and under certain assumptions, achieving proven Pareto optimal solutions while mitigating bias in the trained model. Theoretical analysis indicates that the upper bound on the loss incurred by this method is less than or equal to the loss of the Lagrangian approach, which involves adding a regularization term to the loss function. We demonstrate the efficacy of our model primarily on tabular datasets such as UCI Adult and Heritage Health. When benchmarked against state-of-the-art fairness methods, our model exhibits superior performance, advancing fairness-aware machine learning solutions and bridging the accuracy-fairness gap. The implementation of FairBiNN is available on https://github.com/yazdanimehdi/FairBiNN.

Hybrid electric vehicles (HEVs) are becoming increasingly popular because they can better combine the working characteristics of internal combustion engines and electric motors. However, the minimum fuel consumption of an HEV for a battery electrical balance case under a specific assembly condition and a specific speed curve still needs to be clarified in academia and industry. Regarding this problem, this work provides the mathematical expression of constrained optimal fuel consumption (COFC) from the perspective of constrained reinforcement learning (CRL) for the first time globally. Also, two mainstream approaches of CRL, constrained variational policy optimization (CVPO) and Lagrangian-based approaches, are utilized for the first time to obtain the vehicle's minimum fuel consumption under the battery electrical balance condition. We conduct case studies on the well-known Prius TOYOTA hybrid system (THS) under the NEDC condition; we give vital steps to implement CRL approaches and compare the performance between the CVPO and Lagrangian-based approaches. Our case study found that CVPO and Lagrangian-based approaches can obtain the lowest fuel consumption while maintaining the SOC balance constraint. The CVPO approach converges stable, but the Lagrangian-based approach can obtain the lowest fuel consumption at 3.95 L/100km, though with more significant oscillations. This result verifies the effectiveness of our proposed CRL approaches to the COFC problem.

This paper proposes a Lagrangian approach to find the state equations of a disk rolling on a plane without friction. The approach takes advantage of a symbolic computation to simplify the reasoning.

We present a new way to derive dissipative, optimizing dynamics from the Lagrangian formulation of mechanics. It can be used to obtain both standard and novel neural net dynamics for optimization problems. To demonstrate this we derive standard descent dynamics as well as nonstan(cid:173) dard variants that introduce a computational attention mechanism.

Datasets often contain biases which unfairly disadvantage certain groups, and classifiers trained on such datasets can inherit these biases. In this paper, we provide a mathematical formulation of how this bias can arise. We do so by assuming the existence of underlying, unknown, and unbiased labels which are overwritten by an agent who intends to provide accurate labels but may have biases against certain groups. Despite the fact that we only observe the biased labels, we are able to show that the bias may nevertheless be corrected by re-weighting the data points without changing the labels. We show, with theoretical guarantees, that training on the re-weighted dataset corresponds to training on the unobserved but unbiased labels, thus leading to an unbiased machine learning classifier. Our procedure is fast and robust and can be used with virtually any learning algorithm. We evaluate on a number of standard machine learning fairness datasets and a variety of fairness notions, finding that our method outperforms standard approaches in achieving fair classification.

We present a new way to derive dissipative, optimizing dynamics from the Lagrangian formulation of mechanics. It can be used to obtain both standard and novel neural net dynamics for optimization problems. To demonstrate this we derive standard descent dynamics as well as nonstandard variants that introduce a computational attention mechanism.

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