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This paper presents a conceptual review of our recent advancements on the integration of machine learning and optimization. It focuses on describing new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. 

This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and inter- dependent markets. This coordination represents a classic Stackelberg game and relies on the ex- change of sensitive information between the sys- tem agents. The paper is motivated by the observa- tion that the perturbation introduced by traditional DP mechanisms fundamentally changes the under- lying optimization problem and even leads to un- satisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stack- elberg Mechanism (PPSM), a framework that en- forces the notions of feasibility and fidelity (i.e. near-optimality) of the privacy-preserving informa- tion to the original problem objective. PPSM com- plies with the notion of differential privacy and en- sures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the proposed approach. A full version of this paper [Fioretto et al., 2020b] contains complete proofs and additional discussion on the motivating application.