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Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
Backpropagation (BP), the standard learning algorithm for artificial neural networks, is often considered biologically implausible. In contrast, the standard learning algorithm for predictive coding (PC) models in neuroscience, known as the…
One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like…
A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian…
We consider the problems of computing maximal palindromes and distinct palindromes in a trie. A trie is a natural generalization of a string, which can be seen as a single-path tree. There is a linear-time offline algorithm to compute…
We propose a new General Game Playing (GGP) language called Regular Boardgames (RBG), which is based on the theory of regular languages. The objective of RBG is to join key properties as expressiveness, efficiency, and naturalness of the…
Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), it is still a challenging task to design an efficient binary-coded DE algorithm. Inspired by the learning mechanism of…
A set of preferred records can be obtained from a large database in a multi-criteria setting using various computational methods which either depend on the concept of dominance or on the concept of utility or scoring function based on the…
Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with…
The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…
Many static benchmarks are beginning to saturate: as models rapidly improve, they achieve near-perfect scores on fixed test sets, leaving little headroom to expose genuine model weaknesses -- and even expert-curated challenge sets quickly…
This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…
In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available…