Online optimization is central to display advertising, where we must sequentially allocate ad impressions to maximize the total welfare among advertisers, while respecting various advertiser-specified long-term constraints (e.g., total amount of the ad’s budget that is consumed at the end of the campaign). In this paper, we present the online dual decomposition (ODD) framework for large-scale, online, distributed ad allocation, which combines dual decomposition and on-line convex optimization. ODD allows us to account for the distributed and the online nature of the ad allocation problem and is extensible to a variety of ad allocation problems arising in real-world display advertising systems. Moreover, ODD does not require assumptions about auction dynamics, stochastic or adversarial feedback, or any other characteristics of the ad marketplace. We further provide guarantees for the online solution as measured by bounds on cumulative regret. The regret analysis accounts for the impact of having to estimate constraints in an online setting before they are observed and for the dependence on the smooth-ness with which constraints and constraint violations are generated. We provide an extensive set of results from a large-scale production advertising system at Amazon to validate the framework and compare its behavior to various ad allocation algorithms.