We provide a general framework for solving differentially private stochastic minimax optimization (DP-SMO) problems, which enables the practitioners to bring their own base optimization algorithm and use it as a black-box to obtain the near-optimal privacy-loss trade-off.

We consider an adversarial formulation of the problem ofpredicting a time series with square loss. The aim is to predictan arbitrary sequence of vectors almost as well as the bestsmooth comparator sequence in retrospect. Our approach allowsnatural measures of smoothness such as the squared norm ofincrements. More generally, we consider a linear time seriesmodel and penalize the comparator sequence through the energy ofthe implied driving noise terms. We derive the minimax strategyfor all problems of this type and show that it can be implementedefficiently. The optimal predictions are linear in the previousobservations. We obtain an explicit expression for the regret interms of the parameters defining the problem. For typical,simple definitions of smoothness, the computation of the optimalpredictions involves only sparse matrices. In the case ofnorm-constrained data, where the smoothness is defined in termsof the squared norm of the comparator's increments, we show thatthe regret grows as $T/\sqrt{\lambda_T}$, where $T$ is the lengthof the game and $\lambda_T$ is an increasing limit on comparatorsmoothness.

Identifying the effects of new interventions from data is a significant challenge found across a wide range of the empirical sciences. A well-known strategy for identifying such effects is Pearl's front-door (FD) criterion [

This appendix contains additional material for the paper "Optimistic tree search

Adversarial attacks based on randomized search schemes have obtained state-of-the-art results in black-box robustness evaluation recently.

Traditionally, these would be made according to hard-coded expert heuristics implemented in solvers.

The growing demand for sparse tensor algebra (SpTA) in machine learning and big data has driven the development of various sparse tensor accelerators. However, most existing manually designed accelerators are limited to specific scenarios, and it's time-consuming and challenging to adjust a large number of design factors when scenarios change. Therefore, automating the design of SpTA accelerators is crucial. Nevertheless, previous works focus solely on either mapping (i.e., tiling communication and computation in space and time) or sparse strategy (i.e., bypassing zero elements for efficiency), leading to suboptimal designs due to the lack of comprehensive consideration of both. A unified framework that jointly optimizes both is urgently needed. However, integrating mapping and sparse strategies leads to a combinatorial explosion in the design space(e.g., as large as $O(10^{41})$ for the workload $P_{32 \times 64} \times Q_{64 \times 48} = Z_{32 \times 48}$). This vast search space renders most conventional optimization methods (e.g., particle swarm optimization, reinforcement learning and Monte Carlo tree search) inefficient. To address this challenge, we propose an evolution strategy-based sparse tensor accelerator optimization framework, called SparseMap. SparseMap constructing a more comprehensive design space with the consideration of both mapping and sparse strategy. We introduce a series of enhancements to genetic encoding and evolutionary operators, enabling SparseMap to efficiently explore the vast and diverse design space. We quantitatively compare SparseMap with prior works and classical optimization methods, demonstrating that SparseMap consistently finds superior solutions.

Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc., with gradient-based methods as a typical computational tool. Beyond convex-concave min-max optimization, the solutions found by gradient-based methods may be arbitrarily far from global optima. In this work, we present an algorithmic apparatus for computing globally optimal solutions in convex-non-concave and non-convex-concave min-max optimization. For former, we employ a reformulation that transforms it into a non-concave-convex max-min optimization problem with suitably defined feasible sets and objective function. The new form can be viewed as a generalization of Sion's minimax theorem. Next, we introduce EXOTIC-an Exact, Optimistic, Tree-based algorithm for solving the reformulated max-min problem. EXOTIC employs an iterative convex optimization solver to (approximately) solve the inner minimization and a hierarchical tree search for the outer maximization to optimistically select promising regions to search based on the approximate solution returned by convex optimization solver. We establish an upper bound on its optimality gap as a function of the number of calls to the inner solver, the solver's convergence rate, and additional problem-dependent parameters. Both our algorithmic apparatus along with its accompanying theoretical analysis can also be applied for non-convex-concave min-max optimization. In addition, we propose a class of benchmark convex-non-concave min-max problems along with their analytical global solutions, providing a testbed for evaluating algorithms for min-max optimization. Empirically, EXOTIC outperforms gradient-based methods on this benchmark as well as on existing numerical benchmark problems from the literature. Finally, we demonstrate the utility of EXOTIC by computing security strategies in multi-player games with three or more players.