arXiv research

New algorithm SELECT minimizes satisficing regret in bandits.

Proofs non-realizability of mapping class group via homeomorphisms, resolves Thurston's conjecture.

We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$.

The article enumerates doubly symmetric diagrams for knots up to 18 crossings.

New DP algorithms achieve near-optimal regret bounds for online learning problems.

The pure braid group cannot be realized as area-preserving homeomorphisms.

P. M. Akhmetiev used a controlled version of the stable Hopf invariant to show that any (continuous) map N -> M between stably parallelizable compact n-manifolds, n\ne 1,2,3,7, is realizable in R^{2n}, i.e. the composition of f with an embedding M\subset R^{2n} is C^0-approximable by embeddings. It has been long believ…

New active learning framework for multiclass classification beyond realizability assumption.

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifi…

New method for distributional off-policy evaluation using Bellman residual minimization.

Paper solves the Hurwitz existence problem using fiber products.

Nielsen realization problem for the mapping class group $\text{Mod}(S_g)$ asks whether the natural projection $p_g: \text{Homeo}_+(S_g)\to \text{Mod}(S_g)$ has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of…

In this paper, we will show that the projection $\text{Homeo}^+(D^2_n)\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points in the interior as a set. We also give a new proof of a result o…

Study shows certain mapping class groups cannot be realized as subgroup of homeomorphisms.

Paper tackles MLR prediction error without assuming realizable models.

For every compact surface $S$ of finite type (possibly with boundary components but without punctures), we show that when $n$ is sufficiently large there is no lift $σ$ of the surface braid group $B_n(S)$ to $\operatorname{Diff}(S,n)$, the group of $C^1$ diffeomorphisms preserving $n$ marked points and restricting to t…

We present a short exposition of the following results by S. Parsa. Let $L$ be a graph such that the join $L*\{1,2,3\}$ (i.e. the union of three cones over $L$ along their common bases) piecewise linearly (PL) embeds into $\mathbb R^4$. Then $L$ admits a PL embedding into $\mathbb R^3$ such that any two disjoint cycles…

New algorithm trains ReLU gates provably in linear time.

This study tightens bounds on how GD and SGD generalize in smooth convex optimization problems.

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve perfect reconstruction of the tree cut. In the non-realizable setting, we rely on k…

This paper studies universal rates of ERM for binary classification under agnostic learning.

The study provides error bounds for the generalized Lasso with sub-exponential data.

Generalizes cohomology ring result for combinatorial line arrangements.

Solves open problem on universally consistent online learning with unbounded losses.

The paper explores embedding Ricci flow solutions in flag manifolds.

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate su…

New bandit algorithm works without realizability assumption.

New learner achieves optimal agnostic error in small error regime.

This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estima…

Algorithm learns arbitrary ReLU neurons under Gaussian inputs.

New algorithm optimizes beam and rate allocation in mmWave systems for multiple users.

This article examines five common misunderstandings about case-study research: (1) Theoretical knowledge is more valuable than practical knowledge; (2) One cannot generalize from a single case, therefore the single case study cannot contribute to scientific development; (3) The case study is most useful for generating …

The application of equivalence method to classify Monge-Ampère system leads to three orbits, parabolic case, hyperbolic case and elliptic case wich correspond to three types of Monge-Ampère systems. In this paper we will study the elliptic case and give a presentation of the group as a complex group.

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be ev…

Worst-Case Sensitivity measures model sensitivity to uncertainty set size.

Proposes a new framework for balancing average- and worst-case performance in machine learning.

Solves equality case in isoperimetric inequality for non-convex domains.

Paper improves worst-case regret bounds for RLSVI in reinforcement learning.

Options are generally learned by using an inaccurate environment model (or simulator), which contains uncertain model parameters. While there are several methods to learn options that are robust against the uncertainty of model parameters, these methods only consider either the worst case or the average (ordinary) case…

GenAI improves actuarial practices through case studies.

New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.

A method for logistic regression inference using both internal and external data.

Expanding on a Heisenberg group case for a mathematical proposition.

The book explores alternatives to worst-case analysis for algorithm performance.

Optimizes bond portfolios to avoid worst-case losses.

Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.

Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting system of ordinary differential equations is carefully analy…

Study evaluates and compares numerical differentiation methods on three case studies.