Decision trees are a popular choice of explainable model, but just like neural networks, they suffer from adversarial examples. Existing algorithms for fitting decision trees robust against adversarial examples are greedy heuristics and lack approximation guarantees. In this paper we propose ROCT, a collection of methods to train decision trees that are optimally robust against user-specified attack models. We show that the min-max optimization problem that arises in adversarial learning can be solved using a single minimization formulation for decision trees with 0-1 loss. We propose such formulations in Mixed-Integer Linear Programming and Maximum Satisfiability, which widely available solvers can optimize. We also present a method that determines the upper bound on adversarial accuracy for any model using bipartite matching. Our experimental results demonstrate that the existing heuristics achieve close to optimal scores while ROCT achieves state-of-the-art scores.

Millions of shipping containers filled with goods move around the world every day. Before such a container may enter a trade bloc, the customs agency of the goods' destination country must ensure that it does not contain illegal or mislabeled goods. Due to the high volume of containers, customs agencies make a selection of containers to audit through a risk analysis procedure. Customs agencies perform risk analysis using data sourced from a centralized system that is potentially vulnerable to manipulation and malpractice. Therefore we propose an alternative: DEFEND, a decentralized system that stores data about goods and containers in a secure and privacy-preserving manner. In our system, economic operators make claims to the network about goods they insert into or remove from containers, and encrypt these claims so that they can only be read by the destination country's customs agency. Economic operators also make unencrypted claims about containers with which they interact. Unencrypted claims can be validated by the entire network of customs agencies. Our key contribution is a data partitioning scheme and several protocols that enable such a system to utilize blockchain and its powerful validation principle, while also preserving the privacy of the involved economic operators. Using our protocol, customs agencies can improve their risk analysis and economic operators can get through customs with less delay. We also present a reference implementation built with Hyperledger Fabric and analyze to what extent our implementation meets the requirements in terms of privacy-preservation, security, scalability, and decentralization.

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