A.1 Limitations We propose an approach which exploits object features in addition to scene features for vision-andlanguage navigation (VLN). Our approach is able to utilize object features for better visiolinguistic alignment (see Section 5) despite the domain gap between the images used to train the object detector and VLN data. Specifically, object features are obtained using a Faster R-CNN detector [1] trained on photos from web (Visual Genome [2]), in which objects are typically well framed by the photographer. On the other hand, the VLN datasets used in our experiments contain panoramic images from indoor house scans that capture objects at viewing angles determined by the navigation path. The gap between these two types of data could be eliminated by either fine-tuning or training detector directly on indoor scenes.

In this section we prove the theoretical results around the dual curriculum game and use these results to show approximation bounds for our methods, given that they have reached a Nash equilibrium (NE). The first theorem is the main result that allows us to analyze dual curriculum games. The high-level result says that the NE of a dual curriculum game are approximate NE of the base game from the perspective of any of the individual players, or from the perspective of the joint strategy. Let Bbe the maximum difference between U1t and U2t, and let (π,θ1,θ2) be a NE for G. Then (π,pθ1 + (1 p)θ2) is an approximate NE for the base game with either teacher or for a teacher optimizing their joint objective. More precisely, it is a 2Bp(1 p)-approximate NE when Ut = pU1t + (1 p)U2t, a 2B(1 p)-approximate NE when Ut = U1t, and a 2Bp-approximate NE when Ut = U2t. At a high level, this is true because, for low values of p, the best-response strategies for the individual players can be thought of as approximate-best response strategies for the joint-player, and vis-versa. Since the Nash Equilibrium consists of each of the players playing their own best response, they must be playing an approximate best response for the joint-player. We provide a formal proof below: Proof. Let B be the maximum difference between U1t and U2t, and let (π,θ1,θ2) be a Nash Equilibrium for G. Then consider pθ1 + (1 p)θ2 as a strategy in the base game for the joint player pU1t + (1 p)U2t.

Nonstationarity is prevalent in sequential decision making, which poses a critical challenge to the vast majority of existing approaches developed offline.

Large language models (LLMs) have recently demonstrated great success in generating and understanding natural language. While they have also shown potential beyond the domain of natural language, it remains an open question as to what extent and in which way these LLMs can plan.

Statistical learning under distributional drift remains insufficiently characterized: when each observation alters the data-generating law, classical generalization bounds can collapse. We introduce a new statistical primitive, the reproducibility budget $C_T$, which quantifies a system's finite capacity for statistical reproducibility - the extent to which its sampling process can remain governed by a consistent underlying distribution in the presence of both exogenous change and endogenous feedback. Formally, $C_T$ is defined as the cumulative Fisher-Rao path length of the coupled learner-environment evolution, measuring the total distributional motion accumulated during learning. From this construct we derive a drift-feedback generalization bound of order $O(T^{-1/2} + C_T/T)$, and we prove a matching minimax lower bound showing that this rate is minimax-optimal. Consequently, the results establish a reproducibility speed limit: no algorithm can achieve smaller worst-case generalization error than that imposed by the average Fisher-Rao drift rate $C_T/T$ of the data-generating process. The framework situates exogenous drift, adaptive data analysis, and performative prediction within a common geometric structure, with $C_T$ emerging as the intrinsic quantity measuring distributional motion across these settings.

Abstract-- Hard-constraint trajectory planners often rely on commercial solvers and demand substantial computational resources. Existing soft-constraint methods achieve faster computation, but either (1) decouple spatial and temporal optimization or (2) restrict the search space. T o overcome these limitations, we introduce MIGHTY, a Hermite spline-based planner that performs spatiotemporal optimization while fully leveraging the continuous search space of a spline. In simulation, MIGHTY achieves a 9.3% reduction in computation time and a 13.1% reduction in travel time over state-of-the-art baselines, with a 100% success rate. In hardware, MIGHTY completes multiple high-speed flights up to 6.7 m/s in a cluttered static environment and long-duration flights with dynamically added obstacles. Trajectory planning for autonomous navigation has been extensively studied, with a wide variety of parameterizations and formulations [3], [6], [7], [9], [12], [14]-[17], [19]-[23].