Related papers: Improved bounds for the randomized decision tree c…
Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem.…
We study the average height of random trees generated by leaf-centric binary tree sources as introduced by Zhang, Yang and Kieffer. A leaf-centric binary tree source induces for every $n \geq 2$ a probability distribution on the set of…
We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of arXiv:2103.15993v3 as a model, which is designed for nonsmooth regularized problems,…
It is well-known that the lower bound of iteration complexity for solving nonconvex unconstrained optimization problems is $\Omega(1/\epsilon^2)$, which can be achieved by standard gradient descent algorithm when the objective function is…
There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…
Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…
We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree…
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity measure for primal--dual metrics at pairs of primal and dual…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
We show a new simple algorithm that solves the model-checking problem for recursion schemes: check whether the tree generated by a given higher-order recursion scheme is accepted by a given alternating parity automaton. The algorithm…
We prove that for every parity decision tree of depth $d$ on $n$ variables, the sum of absolute values of Fourier coefficients at level $\ell$ is at most $d^{\ell/2} \cdot O(\ell \cdot \log(n))^\ell$. Our result is nearly tight for small…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on $n$ nodes labeled from an alphabet of size $\sigma$, for which the size of the top DAG is…
We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates. Previous work in unbounded domains…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…
Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…