pwc-archive/papers-with-abstracts huggingface dataset:
On the Stability-Plasticity Dilemma in Continual Meta-Learning: Theory and Algorithm
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We focus on Continual Meta-Learning (CML), which targets accumulating and exploiting meta-knowledge on a sequence of non-i.i.d. tasks. The primary challenge is to strike a balance between stability and plasticity, where a model should be stable to avoid catastrophic forgetting in previous tasks and plastic to learn generalizable concepts from new tasks. To address this, we formulate the CML objective as controlling the average excess risk upper bound of the task sequence, which reflects the trade-off between forgetting and generalization. Based on the objective, we introduce a unified theoretical framework for CML in both static and shifting environments, providing guarantees for various task-specific learning algorithms. Moreover, we first present a rigorous analysis of a bi-level trade-off in shifting environments. To approach the optimal trade-off, we propose a novel algorithm that dynamically adjusts the meta-parameter and its learning rate w.r.t environment change. Empirical evaluations on synthetic and real datasets illustrate the effectiveness of the proposed theory and algorithm.
Faster Query Times for Fully Dynamic $k$-Center Clustering with Outliers
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Given a point set $P\subseteq M$ from a metric space $(M,d)$ and numbers $k, z \in N$, the *metric $k$-center problem with $z$ outliers* is to find a set $C^\ast\subseteq P$ of $k$ points such that the maximum distance of all but at most $z$ outlier points of $P$ to their nearest center in ${C}^\ast$ is minimized. We consider this problem in the fully dynamic model, i.e., under insertions and deletions of points, for the case that the metric space has a bounded doubling dimension $dim$. We utilize a hierarchical data structure to maintain the points and their neighborhoods, which enables us to efficiently find the clusters. In particular, our data structure can be queried at any time to generate a $(3+\varepsilon)$-approximate solution for input values of $k$ and $z$ in worst-case query time $\varepsilon^{-O(dim)}k \log{n} \log\log{\Delta}$, where $\Delta$ is the ratio between the maximum and minimum distance between two points in $P$. Moreover, it allows insertion/deletion of a point in worst-case update time $\varepsilon^{-O(dim)}\log{n}\log{\Delta}$. Our result achieves a significantly faster query time with respect to $k$ and $z$ than the current state-of-the-art by Pellizzoni, Pietracaprina, and Pucci, which uses $\varepsilon^{-O(dim)}(k+z)^2\log{\Delta}$ query time to obtain a $(3+\varepsilon)$-approximation.Submission Number: 13774
$\varepsilon$-fractional core stability in Hedonic Games.
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences. 
According to these preferences, it is desirable that a coalition structure (i.e. a partition of agents into coalitions) satisfies some form of stability. The most well-known and natural of such notions is arguably core-stability. Informally, a partition is core-stable if no subset of agents would like to deviate by regrouping in a so-called core-blocking coalition. Unfortunately, core-stable partitions seldom exist and even when they do, it is often computationally intractable to find one. To circumvent these problems, we propose the notion of $\varepsilon$-fractional core-stability, where at most an $\varepsilon$-fraction of all possible coalitions is allowed to core-block. It turns out that such a relaxation may guarantee both existence and polynomial-time computation. Specifically, we design efficient algorithms returning an $\varepsilon$-fractional core-stable partition, with $\varepsilon$ exponentially decreasing in the number of agents, for two fundamental classes of HGs: Simple Fractional and Anonymous. From a probabilistic point of view, being the definition of $\varepsilon$-fractional core equivalent to requiring that uniformly sampled coalitions core-block with probability lower than $\varepsilon$, we further extend the definition to handle more complex sampling distributions. Along this line, when valuations have to be learned from samples in a PAC-learning fashion, we give positive and negative results on which distributions allow the efficient computation of outcomes that are $\varepsilon$-fractional core-stable with arbitrarily high confidence.Submission Number: 14422
Explainable and Efficient Randomized Voting Rules
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

With a rapid growth in the deployment of AI tools for making critical decisions (or aiding humans in doing so), there is a growing demand to be able to explain to the stakeholders how these tools arrive at a decision. Consequently, voting is frequently used to make such decisions due to its inherent explainability. Recent work suggests that using randomized (as opposed to deterministic) voting rules can lead to significant efficiency gains measured via the distortion framework. However, rules that use intricate randomization can often become too complex to explain to the stakeholders; losing explainability can eliminate the key advantage of voting over black-box AI tools, which may outweigh the efficiency gains.

We study the efficiency gains which can be unlocked by using voting rules that add a simple randomization step to a deterministic rule, thereby retaining explainability. We focus on two such families of rules, randomized positional scoring rules and random committee member rules, and show, theoretically and empirically, that they indeed achieve explainability and efficiency simultaneously to some extent.
Two-Stage Learning to Defer with Multiple Experts
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We study a two-stage scenario for learning to defer with multiple experts, which is crucial in practice for many applications.  In this scenario, a predictor is derived in a first stage by training with a common loss function such as cross-entropy.  In the second stage, a deferral function is learned to assign the most suitable expert to each input.  We design a new family of surrogate loss functions for this scenario both in the score-based and the predictor-rejector settings and prove that they are supported by $H$-consistency bounds, which implies their Bayes-consistency.  Moreover, we show that, for a constant cost function, our two-stage surrogate losses are realizable $H$-consistent. While the main focus of this work is a theoretical analysis, we also report the results of several experiments on CIFAR-10 and SVHN datasets.
$L_2$-Uniform Stability of Randomized Learning Algorithms: Sharper Generalization Bounds and Confidence Boosting
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Exponential generalization bounds with near-optimal rates have recently been established for uniformly stable algorithms~\citep{feldman2019high,bousquet2020sharper}. We seek to extend these best known high probability bounds from deterministic learning algorithms to the regime of randomized learning. One simple approach for achieving this goal is to define the stability for the expectation over the algorithm's randomness, which may result in sharper parameter but only leads to guarantees regarding the on-average generalization error. Another natural option is to consider the stability conditioned on the algorithm's randomness, which is way more stringent but may lead to generalization with high probability jointly over the randomness of sample and algorithm. The present paper addresses such a tension between these two alternatives and makes progress towards relaxing it inside a classic framework of confidence-boosting. To this end, we first introduce a novel concept of $L_2$-uniform stability that holds uniformly over data but in second-moment over the algorithm's randomness. Then as a core contribution of this work, we prove a strong exponential bound on the first-moment of generalization error under the notion of $L_2$-uniform stability. As an interesting consequence of the bound, we show that a bagging-based meta algorithm leads to near-optimal generalization with high probability jointly over the randomness of data and algorithm. We further substantialize these generic results to stochastic gradient descent (SGD) to derive sharper exponential bounds for convex or non-convex optimization with natural time-decaying learning rates, which have not been possible to prove with the existing stability-based generalization guarantees.
Minimax-Optimal Location Estimation
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Location estimation is one of the most basic questions in parametric statistics. 
Suppose we have a known distribution density $f$, and we get $n$ i.i.d. samples from $f(x-\mu)$ for some unknown shift $\mu$.
The task is to estimate $\mu$ to high accuracy with high probability.
The maximum likelihood estimator (MLE) is known to be asymptotically optimal as $n \to \infty$, but what is possible for finite $n$?
In this paper, we give two location estimators that are optimal under different criteria: 1) an estimator that has minimax-optimal estimation error subject to succeeding with probability $1-\delta$ and 2) a confidence interval estimator which, subject to its output interval containing $\mu$ with probability at least $1-\delta$, has the minimum expected squared interval width among all shift-invariant estimators.
The latter construction can be generalized to minimizing the expectation of any loss function on the interval width.Submission Number: 15079
Toward Better PAC-Bayes Bounds for Uniformly Stable Algorithms
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We give sharper bounds for uniformly stable randomized algorithms in a PAC-Bayesian framework, which improve the existing results by up to a factor of $\sqrt{n}$ (ignoring a log factor), where $n$ is the sample size. The key idea is to bound the moment generating function of the generalization gap using concentration of weakly dependent random variables due to Bousquet et al (2020). We introduce an assumption of sub-exponential stability parameter, which allows a general treatment that we instantiate in two applications: stochastic gradient descent and randomized coordinate descent. Our results eliminate the requirement of strong convexity from previous results, and hold for non-smooth convex problems.
Learning Exponential Families from Truncated Samples
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Missing data problems have many manifestations across many scientific fields. A fundamental type of missing data problem arises when samples are \textit{truncated}, i.e., samples that lie in a subset of the support are not observed. Statistical estimation from truncated samples is a classical problem in statistics which dates back to Galton, Pearson, and Fisher. A recent line of work provides the first efficient estimation algorithms for the parameters of a Gaussian distribution and for linear regression with Gaussian noise.

In this paper we generalize these results to log-concave exponential families. We provide an estimation algorithm that shows that \textit{extrapolation} is possible for a much larger class of distributions while it maintains a polynomial sample and time complexity on average. Our algorithm is based on Projected Stochastic Gradient Descent and is not only applicable in a more general setting but is also simpler and more efficient than recent algorithms. Our work also has interesting implications for learning general log-concave distributions and sampling given only access to truncated data.
The Gain from Ordering in Online Learning
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We study fixed-design online learning where the learner is allowed to choose the order of the datapoints in order to minimize their regret (aka self-directed online learning).  We focus on the fundamental task of online linear regression: the learner is given a dataset $X$ with $n$ examples in $d$ dimensions and at step $t$  they select a point $x_t \in X$, predict a value $\widetilde y_t$,  and suffer loss $(\widetilde y_t - w^\ast \cdot x_t)^2$.  The goal is to design algorithms that order the examples and achieve better 
regret  than random- or worst-order online algorithms.

For an arbitrary dataset $X$, we show that, under the Exponential Time Hypothesis, no efficient algorithm can approximate the optimal (best-order)  regret  within a factor of $d^{1/\poly(\log \log d)}$.


We then show that, for structured datasets, we can bypass the above hardness result and achieve nearly optimal regret. When the examples of $X$ are drawn i.i.d.\ from the uniform distribution on the sphere, we present an algorithm based on the greedy heuristic of  selecting ``easiest'' examples first that achieves a $\log d$-approximation of the optimal regret.
Logarithmic Bayes Regret Bounds
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We derive the first finite-time logarithmic Bayes regret upper bounds for Bayesian bandits. In Gaussian bandits, we obtain $O(c_\Delta \log n)$ and $O(c_h \log^2 n)$ bounds for an upper confidence bound algorithm, where $c_h$ and $c_\Delta$ are constants depending on the prior distribution and the gaps of random bandit instances sampled from it, respectively. The latter bound asymptotically matches the lower bound of Lai (1987). Our proofs are a major technical departure from prior works, while being simple and general. To show the generality of our techniques, we apply them to linear bandits. Our results provide insights on the value of prior in the Bayesian setting, both in the objective and as a side information given to the learner. They significantly improve upon existing $\tilde{O}(\sqrt{n})$ bounds, which have become standard in the literature despite the existing lower bounds.
Bandit Task Assignment with Unknown Processing Time
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

This study considers a novel problem setting, referred to as \textit{bandit task assignment}, that incorporates the processing time of each task in the bandit setting. In this problem setting, a player sequentially chooses a set of tasks to start so that the set of processing tasks satisfies a given combinatorial constraint. The reward and processing time for each task follow unknown distributions, values of which are revealed only after the task has been completed. The problem generalizes the stochastic combinatorial semi-bandit problem and the budget-constrained bandit problem. For this problem setting, we propose an algorithm based on upper confidence bounds~(UCB) combined with a phased-update approach. The proposed algorithm admits a gap-dependent regret upper bound of $O(MN(1/\Delta){\log T})$ and a gap-free regret upper bound of $\tilde{O}( \sqrt{MNT} )$, where $N$ is the number of the tasks, $M$ is the maximum number of tasks run at the same time, $T$ is the time horizon, and $\Delta$ is the gap between expected per-round rewards of the optimal and best suboptimal sets of tasks. These regret bounds nearly match lower bounds.
Asymptotically Optimal Quantile Pure Exploration for Infinite-Armed Bandits
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

We study pure exploration with infinitely many bandit arms generated \iid from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$ of being with the top $\eta$-fraction of arms; this is a natural adaptation of the classical PAC guarantee for infinite action sets. We consider both the fixed confidence and fixed budget settings, aiming respectively for optimal \emph{expected} and \emph{fixed} sample complexity.


For fixed confidence, we give an algorithm with expected sample complexity $O\left(\frac{\log (1/\eta)\log (1/\delta)}{\eta\varepsilon^2}\right)$. This is optimal except for the $\log (1/\eta)$ factor, and the $\delta$-dependence closes a quadratic gap in the literature. For fixed budget, we show the asymptotically optimal sample complexity as $\delta\to 0$ is $c^{-1}\log(1/\delta)\big(\log\log(1/\delta)\big)^2$ to leading order; equivalently, the optimal failure probability with exactly $N$ samples decays as 
$\exp\big(-(1\pm o(1))\frac{cN}{\log^2 N}\big)$.
The value of $c$ depends explicitly on the problem parameters (including the unknown arm distribution) through a certain Fisher information distance. Even the strictly super-linear dependence on $\log(1/\delta)$ was not known and resolves a question of Grossman-Moshkovitz (FOCS 2015).
Cascading Bandits: Optimizing Recommendation Frequency in Delayed Feedback Environments
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Delayed feedback is a critical problem in dynamic recommender systems. In practice, the feedback result often depends on the frequency of recommendation. Most existing online learning literature fails to consider optimization of the recommendation frequency, and regards the reward from each successfully recommended message to be equal. In this paper, we consider a novel cascading bandits setting, where individual messages from a selected list are sent to a user periodically. Whenever a user does not like a message, she may abandon the system with a probability positively correlated with the recommendation frequency.  A learning agent needs to learn both the underlying message attraction probabilities and users' abandonment probabilities through the randomly delayed feedback. We first show a dynamic programming solution to finding the optimal message sequence in deterministic scenarios, in which the reward is allowed to vary with different messages. Then we propose a polynomial time UCB-based offline learning algorithm, and discuss its performance by characterizing its regret bound. For the online setting, we propose a learning algorithm which allows adaptive content for a given user. Numerical experiment on AmEx dataset confirms the effectiveness of our algorithms.
On Robust Streaming for Learning with Experts: Algorithms and Lower Bounds
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

In the online learning with experts problem, an algorithm makes predictions about an outcome on each of $T$ days, given a set of $n$ experts who make predictions on each day. The algorithm is given feedback on the outcomes of each day, including the cost of its prediction and the cost of the expert predictions, and the goal is to make a prediction with the minimum cost, compared to the best expert in hindsight. However, often the predictions made by experts or algorithms at some time influence future outcomes, so that the input is adaptively generated. 

In this paper, we study robust algorithms for the experts problem under memory constraints. We first give a randomized algorithm that is robust to adaptive inputs that uses $\widetilde{O}\left(\frac{n}{R\sqrt{T}}\right)$ space for  $M=O\left(\frac{R^2 T}{\log^2 n}\right)$, thereby showing a smooth space-regret trade-off. We then show a space lower bound of $\widetilde{\Omega}\left(\frac{nM}{RT}\right)$ for any randomized algorithm that achieves regret $R$ with probability $1-2^{-\Omega(T)}$, when the best expert makes $M$ mistakes. Our result implies that the natural deterministic algorithm, which iterates through pools of experts until each expert in the pool has erred, is optimal up to polylogarithmic factors. Finally, we empirically demonstrate the benefit of using robust procedures against a white-box adversary that has access to the internal state of the algorithm.
Efficient Batched Algorithm for Contextual Linear Bandits with Large Action Space via Soft Elimination
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

In this paper, we provide the first efficient batched algorithm for contextual linear bandits with large action spaces. Unlike existing batched algorithms that rely on action elimination, which are not implementable for large action sets, our algorithm only uses a linear optimization oracle over the action set to design the policy. The proposed algorithm achieves a regret upper bound $\tilde{O}(\sqrt{T})$ with high probability,  and uses $O(\log\log T)$ batches, matching the lower bound on the number of batches (Gao et al., 2019). When specialized to linear bandits, our algorithm can achieve a high probability gap-dependent regret bound of $\tilde{O}(1/\Delta_{\min})$ with the optimal  $\log T$ number of batches, where $\Delta_{\min}$ is the minimum reward gap between a suboptimal arm and the optimal. Our result is achieved via a novel soft elimination approach, that entails $\text{``}$shaping$\text{"}$ the action sets at each batch so that we can efficiently identify (near) optimal actions.
Near-Linear Time Algorithm for the Chamfer Distance
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\texttt{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the Euclidean or Manhattan distance). The Chamfer distance is a popular measure of dissimilarity between point clouds, used in many machine learning, computer vision, and graphics applications, and admits a straightforward $O(d n^2)$-time brute force algorithm. Further, Chamfer distance is often used as a  proxy for the more computationally demanding Earth-Mover (Optimal Transport) Distance. However, the \emph{quadratic} dependence on $n$ in the running time  makes the naive approach intractable for large datasets.

We overcome this bottleneck and present the first $(1+\epsilon)$-approximate algorithm for estimating Chamfer distance with a near-linear running time. Specifically, our algorithm runs in time $O(nd \log (n)/\epsilon^2)$ and is implementable. Our experiments demonstrate that it is both accurate and fast on large high-dimensional datasets. We believe that our algorithm will open new avenues for analyzing large high-dimensional point clouds. We also give evidence that if the goal is to report a $(1+\epsilon)$-approximate mapping from $A$ to $B$ (as opposed to just its value), then any sub-quadratic  time algorithm is unlikely to exist.
On Slicing Optimality for Mutual Information
Date: 2023-09-21 00:00:00
Proceeding: NeurIPS 2023 11

Measuring dependence between two random variables is of great importance in various domains but is difficult to compute in today's complex environments with high-dimensional data. Recently, slicing methods have shown to be a scalable approach to measuring mutual information (MI) between high-dimensional variables by projecting these variables into one-dimensional spaces. Unfortunately, these methods use uniform distributions of slicing directions, which generally discard informative features between variables and thus lead to inaccurate quantification of dependence. In this paper, we propose a principled framework that searches for an \textit{optimal} distribution of slices for MI. Importantly, we answer theoretical questions about finding the optimal slicing distribution in the context of MI and develop corresponding theoretical analyses. We also develop a practical algorithm, connecting our theoretical results with modern machine learning frameworks. Through comprehensive experiments in benchmark domains, we demonstrate significant gains in our information measure than state-of-the-art baselines.