Neural Information Processing Systems http://nips.cc/

We present an algorithm STRSAGA for efficiently maintaining a machine learning model over data points that arrive over time, quickly updating the model as new training data is observed. We present a competitive analysis comparing the sub-optimality of the model maintained by STRSAGA with that of an offline algorithm that is given the entire data beforehand, and analyze the risk-competitiveness of STRSAGA under different arrival patterns. Our theoretical and experimental results show that the risk of STRSAGA is comparable to that of offline algorithms on a variety of input arrival patterns, and its experimental performance is significantly better than prior algorithms suited for streaming data, such as SGD and SSVRG.

Neural Information Processing Systems http://nips.cc/

Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA).

This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in three cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining four cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

We study online learning in the random-order model, where the multiset of loss functions is chosen adversarially but revealed in a uniformly random order. Building on the batch-to-online conversion by Dong and Yoshida (2023), we show that if an offline algorithm admits a $(1+\varepsilon)$-approximation guarantee and the effect of $\varepsilon$ on its average sensitivity is characterized by a function $φ(\varepsilon)$, then an adaptive choice of $\varepsilon$ yields a small-loss regret bound of $\tilde O(φ^{\star}(\mathrm{OPT}_T))$, where $φ^{\star}$ is the concave conjugate of $φ$, $\mathrm{OPT}_T$ is the offline optimum over $T$ rounds, and $\tilde O$ hides polylogarithmic factors in $T$. Our method requires no regularity assumptions on loss functions, such as smoothness, and can be viewed as a generalization of the AdaGrad-style tuning applied to the approximation parameter $\varepsilon$. Our result recovers and strengthens the $(1+\varepsilon)$-approximate regret bounds of Dong and Yoshida (2023) and yields small-loss regret bounds for online $k$-means clustering, low-rank approximation, and regression. We further apply our framework to online submodular function minimization using $(1\pm\varepsilon)$-cut sparsifiers of submodular hypergraphs, obtaining a small-loss regret bound of $\tilde O(n^{3/4}(1 + \mathrm{OPT}_T^{3/4}))$, where $n$ is the ground-set size. Our approach sheds light on the power of sparsification and related techniques in establishing small-loss regret bounds in the random-order model.

The goal is to learn $A^{*}$ from a single trajectory $X_1,\cdots, X_T$ of {\em dependent or correlated} samples.While the problem is well-studied in the linear case, where $\phi$ is identity, with optimal error rates even for non-mixing systems, existing results in the non-linear case hold only for mixing systems. In this work, we improve existing results for learning nonlinear systems in a number of ways: a) we provide the first offline algorithm that can learn non-linear dynamical systems without the mixing assumption, b) we significantly improve upon the sample complexity of existing results for mixing systems, c) in the much harder one-pass, streaming setting we study a SGD with Reverse Experience Replay (SGD-RER) method, and demonstrate that for mixing systems, it achieves the same sample complexity as our offline algorithm, d) we justify the expansivity assumption by showing that for the popular ReLU link function --- a non-expansive but easy to learn link function with i.i.d.

We present an algorithm STRSAGA for efficiently maintaining a machine learning model over data points that arrive over time, quickly updating the model as new training data is observed. We present a competitive analysis comparing the sub-optimality of the model maintained by STRSAGA with that of an offline algorithm that is given the entire data beforehand, and analyze the risk-competitiveness of STRSAGA under different arrival patterns. Our theoretical and experimental results show that the risk of STRSAGA is comparable to that of offline algorithms on a variety of input arrival patterns, and its experimental performance is significantly better than prior algorithms suited for streaming data, such as SGD and SSVRG.