This paper proposes a Group-DRO enhanced doubly-robust contextual bandit approach to designing optimal policies for loan product offerings.This approach is particularly suited to high-stakes decision-making such as lending decisions, where one must leverage historical data (with inherent biases and uncertainties) to design future policies.By using doubly-robust estimation, we make efficient use of the data and mitigate bias from unknown logging propensities.By incorporating distributional robustness with group-based ambiguity sets, we ensure that the learned policy is insulated against worst-case shifts in each subgroup, thereby protecting the overall performance from crashing if, say, economic conditions change that strongly impact a minority group.By adding fairness constraints such as demographic parity or equal opportunity, we can align the policy with ethical and regulatory standards, ensuring that no group is left behind or unfairly treated by the automated decision process.We present empirical evidence on a small business credit card portfolio, demonstrating significant improvements over standard methods.This proposed framework contributes a step toward responsible AI in finance.

In this paper, we propose an adaptive algorithm with multi-step inertia for solving a convex bilevel optimization problem.Under suitable parameter conditions, we prove that our algorithm converges strongly to some solution of the problem, which is the unique solution to some variational inequality problem.The effectiveness of the proposed algorithm is verified by numerical experiments and compared with other algorithms.

We study a new class of variational inclusion problems in the framework of real Hilbert spaces.We propose two Tseng-type algorithms with inertial extrapolation for solving these problems and carry out the convergence analysis of these two methods.We also give an application of our results to solve convex bilevel optimization problems.

This special issue covers the "International Conference on Variational Analysis and Nonsmooth Optimization," held online on

Training a neural network for semantic segmentation with many images and pixel-level segmentations is a well-established computer-vision technique. When pixel-level segmentations are unavailable, weak supervision or prior information like bounding boxes and the size/shape of objects still enables training a network. Directly including prior knowledge on the segmentations means constraining the network output. This complicates the possible optimization strategies because the regularization then acts on the non-linear neural-network function output and not on the optimization variables. We present a new algorithm to include prior information via constraints on the network output, implemented via projection-based point-to-set distance functions, that are differentiable and always have the same functional form for the derivative. Thus, there is no need to adapt penalty functions or algorithms to various constraints. The distance function's differentiability also avoids issues related to constraining properties typically associated with non-differentiable penalties. We show that by explicitly taking a general neural network structure into account, the Lagrangian for the problem 'naturally' decouples the constraints and neural network, which allows for a gradient computation via backpropagation/adjoint-state as is common in deep learning. We present a suite of constraint sets suitable for segmentation problems. The numerical experiments show that learning from constraint sets applies to the broader imaging sciences, including visual and non-visual imagery, even when training a network for a single example.

We introduce a new concept of approximate solutions to quasi-equilibrium problems (QEP) conceived as approximate fixed points of the implicit selection map associated with this problem. As an application, we consider quasivariational inequalities (QVI) for which we discuss several types of approximations from regularization perspectives to devise a consequential term of approximate solutions. Then we present sensitivity analysis results for parametric versions of (QEP) and (QVI) wherein a recent approximate version of the well-known Lim's Lemma is employed to obtain quantitative stability of approximate solutions to these problems. We finally emphasize that the proposed approximate quasi-equilibrium points converge, from both of the qualitative and quantitative stability aspects, to exact solutions. As a further consequence, we improve some previous stability results of solutions to traffic networks problems with respect to feasible flows under perturbation.