Matthieu C. Martin | Searcharxiv

arXiv2026

Less Traffic, Better Outcomes: Competition-Aware Request Dispatch in Real-Time Ad Exchanges

Real-time bidding (RTB) ad exchanges typically forward nearly all incoming requests to demand-side platforms (DSPs), even though only a small fraction receive bids. This over-distribution weakens auction outcomes: DSPs throttle participation under compute and budget constraints, reducing the effective use of limited bidding capacity. We present a competition-aware request dispatch framework that uses distributional bid prediction and probabilistic forwarding to decide whether each request should be sent to each DSP. The system adapts per-DSP thresholds over time through lightweight policy optimization to track non-stationary market conditions. We evaluate the framework through four sequential online experiments on a production platform serving over 20 billion daily requests. A full multi-DSP deployment reduces DSP request volume under the policy by 34.2% while increasing net revenue by 4.6% (p<0.001) in a recent 14-day window after an initial DSP adaptation period. Further analysis highlights strong heterogeneity across traffic segments and reveals that aggregate metrics can be misleading. Segment-level and per-DSP analyses suggest that the policy surfaces comparative advantages among DSPs, improving monetized outcomes without increasing overall request volume.

cs.AI↗

arXiv2020

PDE-constrained optimal control problems with uncertain parameters using SAGA

We consider an optimal control problem (OCP) for a partial differential equation (PDE) with random coefficients. The optimal control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. For the numerical approximation of this PDE-constrained OCP, we replace the expectation in the objective functional by a suitable quadrature formula and, eventually, discretize the PDE by a Galerkin method. To practically solve such approximate OCP, we propose an importance sampling version the SAGA algorithm, a type of Stochastic Gradient algorithm with a fixed-length memory term, which computes at each iteration the gradient of the loss functional in only one quadrature point, randomly chosen from a possibly non-uniform distribution. We provide a full error and complexity analysis of the proposed numerical scheme. In particular we compare the complexity of the generalized SAGA algorithm with importance sampling, with that of the Stochastic Gradient (SG) and the Conjugate Gradient (CG) algorithms, applied to the same discretized OCP.We show that SAGA converges exponentially in the number of iterations as for a CG algorithm and has a similar asymptotic computational complexity, in terms of computational cost versus accuracy (proportional with the time required if no parallel computing is used). Moreover, it features good pre-asymptotic properties, as shown by our numerical experiments, which makes it appealing in a limited budget context.

math.OC↗