Auto-bidding and budget pacing are formulated as sequential decision-making tasks. While flexible, such a framework faces a fundamental granularity mismatch: decisions are made at a fine temporal scale, while their performance feedback is fully and reliably observable at a much coarser resolution. This manifests as sparse reward signals and delayed feedback, forcing agents to learn from locally noisy and incomplete signals. We address this core challenge by introducing the Trajectory Auto-Regressive Model (TAR), a generative framework that aligns planning resolution with feedback dynamics. Motivated by the insight that coarser temporal aggregation yields denser rewards and less scattered feedback, TAR generates trajectories in a coarse-to-fine manner. It incorporates three key innovations: (1) progressive trajectory generation across multiple temporal scales; (2) latent-space compression via a multi-scale VQVAE to handle heterogeneous feature types; and (3) state-action integration that captures long-term dependencies without auxiliary inverse models. Comprehensive experiments in both sparse-reward and delayed-feedback settings demonstrate that TAR consistently outperforms strong baselines in offline simulations and online deployment, validating its effectiveness in overcoming the granularity mismatch for more stable and robust advertising optimization.

The Guaranteed Delivery (GD) advertising is a crucial component of the online advertising industry, and the allocation of inventory in GD advertising is an important procedure that influences directly the ability of the publisher to fulfill the requirements and increase its revenues. Nowadays, as the requirements of advertisers become more and more diverse and fine-grained, the focus ratio requirement, which states that the portion of allocated impressions of a designated contract on focus media among all possible media should be greater than another contract, often appears in business scenarios. However, taking these requirements into account brings hardness for the GD advertising inventory allocation as the focus ratio requirements involve non-convex multilinear constraints. Existing methods which rely on the convex properties are not suitable for processing this problem, while mathematical programming or constraint-based heuristic solvers are unable to produce high-quality solutions within the time limit. Therefore, we propose a local search framework to address this challenge. It incorporates four new operators designed for handling multilinear constraints and a two-mode algorithmic architecture. Experimental results demonstrate that our algorithm is able to compute high-quality allocations with better business metrics compared to the state-of-the-art mathematical programming or constraint based heuristic solvers. Moreover, our algorithm is able to handle the general multilinear constraints and we hope it could be used to solve other problems in GD advertising with similar requirements.

Contemporary systems of Guaranteed Delivery (GD) advertising work with two different stages, namely, the offline selling stage and the online serving stage. The former deals with contract allocation, and the latter fulfills the impression allocation of signed contracts. Existing work usually handles these two stages separately. For example, contracts are formulated offline without concerning practical situations in the online serving stage. Therefore, we address in this paper a bi-objective contract allocation for GD advertising, which maximizes the impressions, i.e., Ad resource assignments, allocated for the new incoming advertising orders, and at the same time, controls the balance in the inventories. Since the proposed problem is high dimensional and heavily constrained, we design an efficient local search that focuses on the two objectives alternatively. The experimental results indicate that our algorithm outperforms multi-objective evolutionary algorithms and Gurobi, the former of which is commonly applied for multi-objective optimization and the latter of which is a well-known competitive commercial tool.

Guaranteed Delivery (GD) advertising plays an essential part in e-commerce marketing, where the ad publisher signs contracts with advertisers in advance by promising delivery of advertising impressions to fulfill targeting requirements for advertisers. Previous research on GD advertising mainly focused on online serving yet overlooked the importance of contract allocation at the GD selling stage. Traditional GD selling approaches consider impression inventory prediction and contract allocation as two separate stages. However, such a two-stage optimization often leads to inferior contract allocation performance. In this paper, our goal is to reduce this performance gap with a novel end-to-end approach. Specifically, we propose the Neural Lagrangian Selling (NLS) model to jointly predict the impression inventory and optimize the contract allocation of advertising impressions with a unified learning objective. To this end, we first develop a differentiable Lagrangian layer to backpropagate the allocation problem through the neural network and allow direct optimization of the allocation regret. Then, for effective optimization with various allocation targets and constraints, we design a graph convolutional neural network to extract predictive features from the bipartite allocation graph. Extensive experiments show that our approach can improve GD selling performance compared with existing two-stage approaches. Particularly, our optimization layer can outperform the baseline solvers in both computational efficiency and solution quality. To the best of our knowledge, this is the first study to apply the end-to-end prediction and optimization approach for industrial GD selling problems. Our work has implications for general prediction and allocation problems as well.