Related papers: k-flaw Preference Sets
We present Preference Flow Matching (PFM), a new framework for preference-based reinforcement learning (PbRL) that streamlines the integration of preferences into an arbitrary class of pre-trained models. Existing PbRL methods require…
We introduce a generalization of parking functions called $t$-metered $(m,n)$-parking functions, in which one of $m$ cars parks among $n$ spots per hour then leaves after $t$ hours. We characterize and enumerate these sequences for $t=1$,…
We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are $n\in\mathbb{N}$ cars of lengths $\mathbf{y}=(y_1,y_2,\ldots,y_n)\in\mathbb{N}^n$ entering a one-way street…
The selection problem, where one wishes to locate the $k^{th}$ smallest element in an unsorted array of size $n$, is one of the basic problems studied in computer science. The main focus of this work is designing algorithms for solving the…
Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a…
In stochastic combinatorial optimization, algorithms differ in their adaptivity: whether or not they query realized randomness and adapt to it. Dean et al. (FOCS '04) formalize the adaptivity gap, which compares the performance of fully…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
We address the problem of active online assortment optimization problem with preference feedback, which is a framework for modeling user choices and subsetwise utility maximization. The framework is useful in various real-world applications…
Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
The \emph{Shi arrangement} is the set of all hyperplanes in $\mathbb R^n$ of the form $x_j - x_k = 0$ or $1$ for $1 \le j < k \le n$. Shi observed in 1986 that the number of regions (i.e., connected components of the complement) of this…
Aligning large language models with human preferences is critical for creating reliable and controllable AI systems. A human preference can be visualized as a high-dimensional vector where different directions represent trade-offs between…
Preference-based learning aims to align robot task objectives with human values. One of the most common methods to infer human preferences is by pairwise comparisons of robot task trajectories. Traditional comparison-based preference…
In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq…
This work introduces a preference learning method that ensures adherence to given specifications, with an application to autonomous vehicles. Our approach incorporates the priority ordering of Signal Temporal Logic (STL) formulas describing…
We recall that unit interval parking functions of length $n$ are a subset of parking functions in which every car parks in its preference or in the spot after its preference, and Fubini rankings of length $n$ are rankings of $n$ competitors…
We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It…
Linear recursions of degree $k$ are determined by evaluating the sequence of Generalized Fibonacci Polynomials, $\{F_{k,n}(t_1,...,t_k)\}$ (isobaric reflects of the complete symmetric polynomials) at the integer vectors $(t_1,...,t_k)$. If…
We give a bijective proof of the fact that the number of k-prefixes of minimal factorisations of the n-cycle (1...n) as a product of n-1 transpositions is n^{k-1}\binom{n}{k+1}. Rather than a bijection, we construct a surjection with fibres…
Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any classical parking function can be uniquely described as a…