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A second order regret bound for NormalHedge

arXiv.org Machine Learning

We consider the problem of prediction with expert advice for ``easy'' sequences. We show that a variant of NormalHedge enjoys a second-order $ฮต$-quantile regret bound of $O\big(\sqrt{V_T \log(V_T/ฮต)}\big) $ when $V_T > \log N$, where $V_T$ is the cumulative second moment of instantaneous per-expert regret averaged with respect to a natural distribution determined by the algorithm. The algorithm is motivated by a continuous time limit using Stochastic Differential Equations. The discrete time analysis uses self-concordance techniques.





Co-PLNet: A Collaborative Point-Line Network for Prompt-Guided Wireframe Parsing

arXiv.org Machine Learning

Wireframe parsing aims to recover line segments and their junctions to form a structured geometric representation useful for downstream tasks such as Simultaneous Localization and Mapping (SLAM). Existing methods predict lines and junctions separately and reconcile them post-hoc, causing mismatches and reduced robustness. We present Co-PLNet, a point-line collaborative framework that exchanges spatial cues between the two tasks, where early detections are converted into spatial prompts via a Point-Line Prompt Encoder (PLP-Encoder), which encodes geometric attributes into compact and spatially aligned maps. A Cross-Guidance Line Decoder (CGL-Decoder) then refines predictions with sparse attention conditioned on complementary prompts, enforcing point-line consistency and efficiency. Experiments on Wireframe and YorkUrban show consistent improvements in accuracy and robustness, together with favorable real-time efficiency, demonstrating our effectiveness for structured geometry perception.


Locally Optimal Solutions to Constraint Displacement Problems via Path-Obstacle Overlaps

arXiv.org Artificial Intelligence

We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle displacements to enable a feasible path for the robot. In the second stage, these obstacles are displaced to make the computed robot trajectory feasible, that is, collision-free. Several examples are provided that successfully demonstrate our approach on two distinct classes of constraint displacement problems. Introduction As humans, we encounter various situations in our day to day life in which we alter the location of objects - opening closed doors, repositioning chairs or other movable objects, clear objects while picking an object of interest from a cluttered table-top. As opposed to avoiding each object, altering or displacing these objects or constraints allow us to expand the solution space of feasible paths. In such situations, constraints, such as movable obstacles, may be cleared to find feasible paths. Manipulators often need to rearrange or move obstacles aside to accomplish a given set of tasks - a futuristic robot cooking dinner at home, manipulation in industrial settings, shelves replenishment in a grocery store. Service robots may need to reposition chairs or other movable objects to accomplish a task. A robot may need to plan a path through dynamic obstacles as they might clear the path while moving. We define a constraint displacement problem as one that finds a feasible path by displacing constraints while minimizing a problem-specific objective function.


A Best-of-Both-Worlds Proof for Tsallis-INF without Fenchel Conjugates

arXiv.org Machine Learning

The multi-armed bandit problem is a classic framework for sequential decision-making under uncertainty, encapsulating the fundamental trade-off between exploration and exploitation. This problem is typically studied in two primary settings: the stochastic setting, where the loss for each arm is drawn independently and identically from a fixed distribution, and the adversarial setting, where an arbitrary and potentially adaptive sequence of losses is generated. While numerous algorithms have been developed that are optimal for one of these settings, a significant challenge has been to design a single algorithm that performs well in both, without prior knowledge of the environment. Such an algorithm is said to have a "best-of-both-worlds" guarantee. By choosing an appropriate regularization function, a Follow-The-Regularized-Leader (FTRL) [Gordon, 1999a,b, Shalev-Shwartz and Singer, 2006a,b, Abernethy et al., 2008, Hazan and Kale, 2008] approach can achieve low regret in the adversarial setting while adapting to the easier stochastic setting to attain near-optimal, logarithmically-scaling regret, that is, a best-of-both-worlds guarantee. The Tsallis-INF algorithm [Audibert and Bubeck, 2009], when used in a FTRL algorithm was shown to have this property by Zimmert and Seldin [2021]. The aim of this note is to provide a concise and self-contained proof of this guarantee for the Tsallis-INF algorithm. In particular, the derivation relies on standard and modern techniques from online convex optimization, particularly the FTRL regret lemma and its local norm analysis.