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When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the…
Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance…
Machine learning algorithms enable advanced decision making in contemporary intelligent systems. Research indicates that there is a tradeoff between their model performance and explainability. Machine learning models with higher performance…
Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of…
Reinforcement learning (RL) algorithms assume that users specify tasks by manually writing down a reward function. However, this process can be laborious and demands considerable technical expertise. Can we devise RL algorithms that instead…
The security provided by a firewall for a computer network almost completely depends on the rules it enforces. For over a decade, it has been a well-known and unsolved problem that the quality of many firewall rule sets is insufficient.…
In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…
There is no free lunch, no single learning algorithm that will outperform other algorithms on all data. In practice different approaches are tried and the best algorithm selected. An alternative solution is to build new algorithms on demand…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
In many prediction problems, the predictive model affects the distribution of the prediction target. This phenomenon is known as performativity and is often caused by the behavior of individuals with vested interests in the outcome of the…
Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed…
Given the importance of accurate team rankings in American college football (CFB) -- due to heavy title and playoff implications -- strides have been made to improve evaluation metrics across statistical categories, going from basic…
The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
We study the settings where we are given a function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our approach allows…