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Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…
The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…
In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily…
Stochastic games are a natural model for the synthesis of controllers confronted to adversarial and/or random actions. In particular, $\omega$-regular games of infinite length can represent reactive systems which are not expected to reach a…
The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
Until recently, the fastest distributed MIS algorithm, even for simple graphs, e.g., unoriented trees has been the simple randomized algorithm discovered the 80s. This algorithm (commonly called Luby's algorithm) computes an MIS in $O(\log…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
Learning a regression function using censored or interval-valued output data is an important problem in fields such as genomics and medicine. The goal is to learn a real-valued prediction function, and the training output labels indicate an…
Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective.…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments,…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting. In this article, we relax the notion of accepting run by allowing a certain quantity…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…