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In this article, we present a detailed review of current practices and state-of-the-art methodologies in the field of differential privacy (DP), with a focus of advancing DP’s deployment in real-world applications. Key points and high-level contents of the article were originated from the discussions from “Differential Privacy (DP): Challenges Towards the Next Frontier,” a workshop held in July 2022 with experts from industry, academia, and the public sector seeking answers to broad questions pertaining to privacy and its implications in the design of industry-grade systems.This article aims to provide a reference point for the algorithmic and design decisions within the realm of privacy, highlighting important challenges and potential research directions. Covering a wide spectrum of topics, this article delves into the infrastructure needs for designing private systems, methods for achieving better privacy/utility trade-offs, performing privacy attacks and auditing, as well as communicating privacy with broader audiences and stakeholders. 

Composition is one of the most important properties of differential privacy (DP), as it allows algorithm designers to build complex private algorithms from DP primitives. We consider precise composition bounds of the overall privacy loss for exponential mechanisms, one of the fundamental classes of mechanisms in DP. We give explicit formulations of the optimal privacy loss for both the adaptive and non-adaptive settings. For the non-adaptive setting in which each mechanism has the same privacy parameter, we give an efficiently computable formulation of the optimal privacy loss. Furthermore, we show that there is a difference in the privacy loss when the exponential mechanism is chosen adaptively versus non-adaptively. To our knowledge, it was previously unknown whether such a gap existed for any DP mechanisms with fixed privacy parameters, and we demonstrate the gap for a widely used class of mechanism in a natural setting. We then improve upon the best previously known upper bounds for adaptive composition of exponential mechanisms with efficiently computable formulations and show the improvement.