Full Swap Regret and Discretized Calibration

• URL: http://arxiv.org/abs/2502.09332v1
• Date: Thu, 13 Feb 2025 13:49:52 GMT
• Title: Full Swap Regret and Discretized Calibration
• Authors: Maxwell Fishelson, Robert Kleinberg, Princewill Okoroafor, Renato Paes Leme, Jon Schneider, Yifeng Teng,
• Abstract summary: We study the problem of minimizing swap regret in structured normal-form games. We introduce a new online learning problem we call emphfull swap regret minimization We also apply these tools to the problem of online forecasting to calibration error.
• Score: 18.944031222413294
• License:
• Abstract: We study the problem of minimizing swap regret in structured normal-form games. Players have a very large (potentially infinite) number of pure actions, but each action has an embedding into $d$-dimensional space and payoffs are given by bilinear functions of these embeddings. We provide an efficient learning algorithm for this setting that incurs at most $\tilde{O}(T^{(d+1)/(d+3)})$ swap regret after $T$ rounds. To achieve this, we introduce a new online learning problem we call \emph{full swap regret minimization}. In this problem, a learner repeatedly takes a (randomized) action in a bounded convex $d$-dimensional action set $\mathcal{K}$ and then receives a loss from the adversary, with the goal of minimizing their regret with respect to the \emph{worst-case} swap function mapping $\mathcal{K}$ to $\mathcal{K}$. For varied assumptions about the convexity and smoothness of the loss functions, we design algorithms with full swap regret bounds ranging from $O(T^{d/(d+2)})$ to $O(T^{(d+1)/(d+2)})$. Finally, we apply these tools to the problem of online forecasting to minimize calibration error, showing that several notions of calibration can be viewed as specific instances of full swap regret. In particular, we design efficient algorithms for online forecasting that guarantee at most $O(T^{1/3})$ $\ell_2$-calibration error and $O(\max(\sqrt{\epsilon T}, T^{1/3}))$ \emph{discretized-calibration} error (when the forecaster is restricted to predicting multiples of $\epsilon$).

Related papers

• Sparsity-Based Interpolation of External, Internal and Swap Regret [4.753557469026313]
  This paper studies the comparator of several performance metrics via $phi$-regret minimization. We present a single algorithm achieving the instance-adaptive $phi$-regret bound. Building on the classical reduction from $phi$-regret minimization to external regret minimization, our main idea is to further convert the latter to online linear regression.
  arXiv  Detail & Related papers  (2025-02-06T22:47:52Z)
• Near-Optimal Algorithms for Omniprediction [6.874077229518565]
  We give near-optimal learning algorithms for omniprediction, in both the online and offline settings. Online learning algorithm achieves near-optimal complexity across a number of measures. offline learning algorithm returns an efficient $(mathcalL_mathrmBV,mathcalH,varepsilon(m)$)
  arXiv  Detail & Related papers  (2025-01-28T02:58:37Z)
• Non-stationary Projection-free Online Learning with Dynamic and Adaptive Regret Guarantees [36.746745619968024]
  We investigate non-stationary projection-free online learning, and choose dynamic regret and adaptive regret to measure the performance. Our results are the first general-case dynamic regret bounds for projection-free online learning, and can recover the existing $mathcalO(T3/4)$ static regret. We propose a projection-free method to attain an $tildemathcalO(tau3/4)$ adaptive regret bound for any interval with length $tau.
  arXiv  Detail & Related papers  (2023-05-19T15:02:10Z)
• Near-Optimal Algorithms for Private Online Optimization in the Realizable Regime [74.52487417350221]
  We consider online learning problems in the realizable setting, where there is a zero-loss solution. We propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds.
  arXiv  Detail & Related papers  (2023-02-27T21:19:24Z)
• Eluder-based Regret for Stochastic Contextual MDPs [43.19667415823089]
  We present the E-UC$3$RL algorithm for regret minimization in Contextual Markov Decision Processes (CMDPs) Our algorithm is efficient (assuming efficient offline regression oracles) and enjoys a regret guarantee of $ widetildeO(H3 sqrtT |S| |A|d_mathrmE(mathcalP)$.
  arXiv  Detail & Related papers  (2022-11-27T20:38:47Z)
• Online Convex Optimization with Continuous Switching Constraint [78.25064451417082]
  We introduce the problem of online convex optimization with continuous switching constraint. We show that, for strongly convex functions, the regret bound can be improved to $O(log T)$ for $S=Omega(log T)$, and $O(minT/exp(S)+S,T)$ for $S=O(log T)$.
  arXiv  Detail & Related papers  (2021-03-21T11:43:35Z)
• Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization [51.23789922123412]
  We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions admit a "pseudo-1d" structure. We show a lower bound of $min(sqrtdT, T3/4)$ for the regret of any algorithm, where $T$ is the number of rounds. We propose a new algorithm sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively.
  arXiv  Detail & Related papers  (2021-02-15T08:16:51Z)
• Revisiting Smoothed Online Learning [70.09792747315323]
  We investigate the problem of smoothed online learning, in which the online learner suffers both a hitting cost and a switching cost. To bound the competitive ratio, we assume the hitting cost is known to the learner in each round, and investigate the greedy algorithm which simply minimizes the weighted sum of the hitting cost and the switching cost.
  arXiv  Detail & Related papers  (2021-02-13T14:15:55Z)
• Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints [94.76881135901753]
  We consider two popular limited adaptivity models: batch learning model and rare policy switch model. Our proposed LSVI-UCB-Batch algorithm achieves an $tilde O(sqrtd3H3T + dHT/B)$ regret. For the rare policy switch model, our proposed LSVI-UCB-RareSwitch algorithm enjoys an $tilde O(sqrtd3H3T[1+T/(dH)]dH/B)$ regret.
  arXiv  Detail & Related papers  (2021-01-06T18:56:07Z)
• Taking a hint: How to leverage loss predictors in contextual bandits? [63.546913998407405]
  We study learning in contextual bandits with the help of loss predictors. We show that the optimal regret is $mathcalO(minsqrtT, sqrtmathcalETfrac13)$ when $mathcalE$ is known.
  arXiv  Detail & Related papers  (2020-03-04T07:36:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.