In addition to solving (1), we also wish topreserve privacyfor the people who contributed to the dataset Z.

Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is arbitrarily time-varying. As no algorithm can guarantee low regret simultaneously against all comparator sequences, handling this setting requires moving from minimax optimality to comparator adaptivity. That is, sensible regret bounds should depend on certain complexity measures of the comparator relative to one's prior knowledge. This paper achieves a new type of such adaptive regret bounds leveraging a sparse coding framework. The complexity of the comparator is measured by its energy and its sparsity on a user-specified dictionary, which offers considerable versatility. For example, equipped with a wavelet dictionary, our framework improves the state-of-the-art bound (Jacobsen & Cutkosky, 2022) by adapting to both ($i$) the magnitude of the comparator average $||\bar u||=||\sum_{t=1}^Tu_t/T||$, rather than the maximum $\max_t||u_t||$; and ($ii$) the comparator variability $\sum_{t=1}^T||u_t-\bar u||$, rather than the uncentered sum $\sum_{t=1}^T||u_t||$. Furthermore, our proof is simpler due to decoupling function approximation from regret minimization.

One of the most popular optimization algorithms is Adam [Kingma and Ba, 2014].

We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators $u_{1},\ldots,u_{T}$ in $\mathcal{W}\subseteq\mathbb{R}^{d}$ is equivalent to competing with a fixed comparator function $u:[1,T]\to \mathcal{W}$, we frame dynamic regret minimization as a static regret problem in a function space. By carefully constructing a suitable function space in the form of a Reproducing Kernel Hilbert Space (RKHS), our reduction enables us to recover the optimal $R_{T}(u_{1},\ldots,u_{T}) = \mathcal{O}(\sqrt{\sum_{t}\|u_{t}-u_{t-1}\|T})$ dynamic regret guarantee in the setting of linear losses, and yields new scale-free and directionally-adaptive dynamic regret guarantees. Moreover, unlike prior dynamic-to-static reductions -- which are valid only for linear losses -- our reduction holds for any sequence of losses, allowing us to recover $\mathcal{O}\big(\|u\|^2+d_{\mathrm{eff}}(λ)\ln T\big)$ bounds in exp-concave and improper linear regression settings, where $d_{\mathrm{eff}}(λ)$ is a measure of complexity of the RKHS. Despite working in an infinite-dimensional space, the resulting reduction leads to algorithms that are computable in practice, due to the reproducing property of RKHSs.

This paper addresses online learning with ``corrupted'' feedback. Our learner is provided with potentially corrupted gradients $\tilde g_t$ instead of the ``true'' gradients $g_t$. We make no assumptions about how the corruptions arise: they could be the result of outliers, mislabeled data, or even malicious interference. We focus on the difficult ``unconstrained'' setting in which our algorithm must maintain low regret with respect to any comparison point $u \in \mathbb{R}^d$. The unconstrained setting is significantly more challenging as existing algorithms suffer extremely high regret even with very tiny amounts of corruption (which is not true in the case of a bounded domain). Our algorithms guarantee regret $ \|u\|G (\sqrt{T} + k) $ when $G \ge \max_t \|g_t\|$ is known, where $k$ is a measure of the total amount of corruption. When $G$ is unknown we incur an extra additive penalty of $(\|u\|^2+G^2) k$.

Microspine grippers are small spines commonly found on insect legs that reinforce surface interaction by engaging with asperities to increase shear force and traction. An array of such microspines, when integrated into the limbs or undercarriage of a robot, can provide the ability to maneuver uneven terrains, traverse inclines, and even climb walls. Conformability and adaptability of soft robots makes them ideal candidates for these applications involving traversal of complex, unstructured terrains. However, there remains a real-life realization gap for soft locomotors pertaining to their transition from controlled lab environment to the field by improving grip stability through effective integration of microspines. We propose a passive, compliant microspine stacked array design to enhance the locomotion capabilities of mobile soft robots, in our case, ones that are motor tendon actuated. We offer a standardized microspine array integration method with effective soft-compliant stiffness integration, and reduced complexity resulting from a single actuator passively controlling them. The presented design utilizes a two-row, stacked microspine array configuration that offers additional gripping capabilities on extremely steep/irregular surfaces from the top row while not hindering the effectiveness of the more frequently active bottom row. We explore different configurations of the microspine array to account for changing surface topologies and enable independent, adaptable gripping of asperities per microspine. Field test experiments are conducted on various rough surfaces including concrete, brick, compact sand, and tree roots with three robots consisting of a baseline without microspines compared against two robots with different combinations of microspine arrays. Tracking results indicate that the inclusion of microspine arrays increases planar displacement on average by 15 and 8 times.

Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence u_1,\ldots,u_T is arbitrarily time-varying. As no algorithm can guarantee low regret simultaneously against all comparator sequences, handling this setting requires moving from minimax optimality to comparator adaptivity. That is, sensible regret bounds should depend on certain complexity measures of the comparator relative to one's prior knowledge. This paper achieves a new type of such adaptive regret bounds leveraging a sparse coding framework. The complexity of the comparator is measured by its energy and its sparsity on a user-specified dictionary, which offers considerable versatility.