We consider a multiobjective multiarmed bandit problem with lexicographically ordered objectives. In this problem, the goal of the learner is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multidimensional for…
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48 results for “lexicographic differentiation”
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp…
We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree of a lexicographic parametrisation of such a knot. This allows us to transform this problem into a study of real algebraic trigonal plane c…
We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely many lexicographically ordered levels of events and for eve…
The language of maximal lexicographic representatives of elements in the positive braid monoid with generators is a regular language. We describe with great detail the smallest Finite State Automaton accepting such language, and study the proportion of elements of length whose maximal lexicographic repres…
The paper proposes a method to infer multi-objective rewards from preferences.
problem Modeling preferences based on multiple, often competing objectives.
method Modeling priorities lexicographically and inferring multi-objective rewards from observed preferences.
result Lexicographically-ordered rewards provide a better understanding of preferences and improve policies.
Nonsmooth High-Order Averaging Theory with Application to Extremum Seeking Optimization and Controlmath.OC
New theory for nonsmooth systems helps optimize and control complex functions.
problem Optimizing and controlling systems with nonsmooth functions.
method Higher-order averaging theory with nonsmooth near-identity transformation and lexicographic differentiation.
result Closed formula for nonsmooth first and second-order averaging.
New fairness concept extends minimax fairness to lexicographic fairness.
problem Fairness in supervised learning, especially lexicographic fairness.
method Introduced approximate lexifairness, derived algorithms for finding solutions, and proved generalization bounds.
result Proved that approximate lexifairness on training data implies approximate lexifairness on true distribution.
We introduce a rich model for multi-objective clustering with lexicographic ordering over objectives and a slack. The slack denotes the allowed multiplicative deviation from the optimal objective value of the higher priority objective to facilitate improvement in lower-priority objectives. We then propose an algorithm …
With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous mo…
Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theorymath.AT
New connection found between shape reconstruction methods and persistent homology.
problem Connecting shape reconstruction methods with persistent homology.
method Wrap complexes and lexicographic optimal homologous cycles.
result Lexicographically optimal homologous cycles are supported on Wrap complexes.
The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We show that the finite subset …
Let N and P be smooth manifolds of dimensions n and p (n>=p>=2). Let Omega^{I}(N,P) denote an open subspace of J(N,P) which consists of all Boardman submanifolds Sigma^{J}(N,P) with J=< I in the lexicographic order. We will prove the homotopy principle in the existence level for Omega^{I}(N,P).
Groups with specific curvature have a regular language of geodesics.
problem Understanding the language of geodesics in non-positively curved triangle groups.
method Proving finitely many cone types and regularity of geodesic languages.
result The language of lexicographically first geodesics is regular and satisfies the fellow traveller property.
Double Fairness Policy Learning: Integrating Action Fairness and Outcome Fairness in Decision-makingstat.ML
DFL framework improves action and outcome fairness in policy learning.
problem Fairness in policy learning, especially action and outcome fairness.
method Integrates action and outcome fairness into a multi-objective optimization problem using a lexicographic weighted Tchebyshev method.
result DFL framework improves both action and outcome fairness with minimal value reduction.
A proof of imitation of Wasserstein inverse reinforcement learning for multi-objective optimizationcs.LG
Proof shows imitation of expert's reward and solutions in multi-objective optimization.
problem Multi-objective optimization with reward and solution imitation.
method Wasserstein inverse reinforcement learning.
result Wasserstein inverse reinforcement learning enables imitation of expert's reward and solutions in multi-objective optimization.
Thin Tree Positionmath.CO
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…
Let and be smooth closed manifolds of dimensions and respectively. Given a Thom-Boardman symbol , a smooth map is called an -regular map if and only if the Thom-Boardman symbol of each singular point of is not greater than in the lexicographic order. We will represent the gr…
In the following text we compute possible heights of (Alexandroff square), (unit square with lexicographic order topology) and (unit square with induced topology of Euclidean plane). We prove , $P_h(\m…
New method allows backtesting of systemic risk forecasts.
problem Systemic risk measures are not elitable and identifiable, making backtesting impossible.
method Introduces multi-objective elicitability and Diebold--Mariano type tests.
result Proposes a traffic-light approach for backtesting.
The study explores properties and mutations in oriented matroids, proving new results on Euclidean and non-Euclidean structures.
problem Investigating the Euclidean and non-Euclidean properties of oriented matroids.
method Analyzing the minimum number of mutations, using lexicographic extensions, and mutation-flips to prove properties.
result For rank 4 uniform oriented matroids, the minimum number of mutations adjacent to an element is at most 3.
Study a specific line arrangement and compute its fundamental group via braid monodromy.
problem Compute the fundamental group of a specific line arrangement's complement.
method Use braid monodromy to compute the fundamental group.
result The resulting presentation of the fundamental group coincides with the modified Artin presentation.
Deep learning agent improves pedestrian navigation in urban environments.
problem Autonomous driving among pedestrians in urban areas.
method Multi-objective deep reinforcement learning using a deep Q-learning variant.
result The multi-objective DQN agent outperforms single-objective DQN in various environments.
Given a compact geodesic space we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic -metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexe…
Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict coincidences for limiting homological densities of various sequences $\mathcal{Z}^{(d_1,\…
The paper finds formulas for word lengths and conjugacy classes in surface groups.
problem Finding formulas for word lengths and conjugacy classes in surface groups.
method Investigating symmetric presentations and normal forms of conjugacy classes.
result Derives three formulae for word lengths and provides efficient algorithms for conjugacy problems.
We present a new procedure to determine the growth function of a homogeneous Garside monoid, with respect to the finite generating set formed by the atoms. In particular, we present a formula for the growth function of each Artin--Tits monoid of spherical type (hence of each braid monoid) with respect to the standard g…
This work tackles asymmetric community estimation in multi-layer directed networks.
problem Estimating different numbers of sender and receiver communities in multi-layer directed networks.
method Proposes a goodness-of-fit test based on the largest singular value of an aggregated normalized residual matrix.
result Develops sequential and ratio-based testing procedures to consistently determine true sender and receiver community numbers.
New RL algorithm ensures stable, replicable policies.
problem Stability and replicability issues in RL algorithms.
method Introduced weak and strong forms of list replicability, developed a novel planning strategy, and tested state reachability.
result Proved efficient tabular RL algorithm with polynomial list complexity.
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…
In this paper we give explicit formulas of differential characteristic classes of principal -bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…
We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differenti…
We generalize stochastic smoothing for gradient estimation of non-differentiable functions.
problem Gradient estimation for non-differentiable functions.
method Developed a general framework for relaxation and gradient estimation of non-differentiable black-box functions using stochastic smoothing with reduced assumptions.
result Empirically validated the effectiveness of variance reduction strategies for various non-differentiable tasks.
The paper proves Gorenstein contractions for multiscale differentials on nodal curves.
problem Proving Gorenstein contractions for multiscale differentials on nodal curves.
method Addressing the conjecture by Ranganathan and Wise, showing contractions level by level.
result Multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down.
Classifies components of strata of k-differentials on Riemann surfaces.
problem Classifying connected components of strata of k-differentials.
method Developed new techniques to study connected components of strata of k-differentials for general k.
result Complete classification of connected components of the strata of quadratic differentials with arbitrary poles.
Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result Monotonic differentiable sorting networks improve upon previous methods.
Lecture notes introduce differential geometry using sheaves and differential operators.
problem Exploring differential geometry concepts.
method Using sheaves, differential operators, and horizontal subbundles.
result Presented an approach to fundamental differential geometry structures.
Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differentia…
Paper defines quasi-Strebel structures for meromorphic k-differentials and proves their existence.
problem Existence of quasi-Strebel structures for meromorphic k-differentials.
method Introduced quasi-Strebel structures and proved their existence for meromorphic k-differentials.
result Every differential of even order k > 2 satisfying certain conditions admits a quasi-Strebel structure.
Finite intersection numbers between horizontal foliations of quadratic differentials.
problem Intersection properties of horizontal foliations in quadratic differentials.
method Joint continuity of intersection number in -norm.
result Intersection number is finite and jointly continuous.
We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. We also consider the conditions of any differential ensuring …
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds admit a unique differential, coinciding with the usual one. Thus smooth manifolds fo…
Paper solves a class of differential equations with specific solutions.
problem Identifying solutions to a class of nonlinear ODEs.
method Solves using a proposed side condition involving a third-order linear ODE.
result New closed and integral-form solutions for the Tzitzeica curve equation.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra a…
By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology …
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomo…