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Transfer learning has been demonstrated to be successful and essential in diverse applications, which transfers knowledge from related but different source domains to the target domain. Online transfer learning(OTL) is a more challenging problem where the target data arrive in an online manner. Most OTL methods combine source classifier and target classifier directly by assigning a weight to each classifier, and adjust the weights constantly. However, these methods pay little attention to reducing the distribution discrepancy between domains. In this paper, we propose a novel online transfer learning method which seeks to find a new feature representation, so that the marginal distribution and conditional distribution discrepancy can be online reduced simultaneously. We focus on online transfer learning with multiple source domains and use the Hedge strategy to leverage knowledge from source domains. We analyze the theoretical properties of the proposed algorithm and provide an upper mistake bound. Comprehensive experiments on two real-world datasets show that our method outperforms state-of-the-art methods by a large margin.
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Transfer learning techniques have been widely used in the reality that it is difficult to obtain sufficient labeled data in the target domain, but a large amount of auxiliary data can be obtained in the relevant source domain. But most of the existing methods are based on offline data. In practical applications, it is often necessary to face online learning problems in which the data samples are achieved sequentially. In this paper, We are committed to applying the ensemble approach to solving the problem of online transfer learning so that it can be used in anytime setting. More specifically, we propose a novel online transfer learning framework, which applies the idea of online bagging methods to anytime transfer learning problems, and constructs strong classifiers through online iterations of the usefulness of multiple weak classifiers. Further, our algorithm also provides two extension schemes to reduce the impact of negative transfer. Experiments on three real data sets show that the effectiveness of our proposed algorithms.
In the stochastic online vector balancing problem, vectors $v_1,v_2,ldots,v_T$ chosen independently from an arbitrary distribution in $mathbb{R}^n$ arrive one-by-one and must be immediately given a $pm$ sign. The goal is to keep the norm of the discrepancy vector, i.e., the signed prefix-sum, as small as possible for a given target norm. We consider some of the most well-known problems in discrepancy theory in the above online stochastic setting, and give algorithms that match the known offline bounds up to $mathsf{polylog}(nT)$ factors. This substantially generalizes and improves upon the previous results of Bansal, Jiang, Singla, and Sinha (STOC 20). In particular, for the Koml{o}s problem where $|v_t|_2leq 1$ for each $t$, our algorithm achieves $tilde{O}(1)$ discrepancy with high probability, improving upon the previous $tilde{O}(n^{3/2})$ bound. For Tusn{a}dys problem of minimizing the discrepancy of axis-aligned boxes, we obtain an $O(log^{d+4} T)$ bound for arbitrary distribution over points. Previous techniques only worked for product distributions and gave a weaker $O(log^{2d+1} T)$ bound. We also consider the Banaszczyk setting, where given a symmetric convex body $K$ with Gaussian measure at least $1/2$, our algorithm achieves $tilde{O}(1)$ discrepancy with respect to the norm given by $K$ for input distributions with sub-exponential tails. Our key idea is to introduce a potential that also enforces constraints on how the discrepancy vector evolves, allowing us to maintain certain anti-concentration properties. For the Banaszczyk setting, we further enhance this potential by combining it with ideas from generic chaining. Finally, we also extend these results to the setting of online multi-color discrepancy.
We study the online discrepancy minimization problem for vectors in $mathbb{R}^d$ in the oblivious setting where an adversary is allowed fix the vectors $x_1, x_2, ldots, x_n$ in arbitrary order ahead of time. We give an algorithm that maintains $O(sqrt{log(nd/delta)})$ discrepancy with probability $1-delta$, matching the lower bound given in [Bansal et al. 2020] up to an $O(sqrt{log log n})$ factor in the high-probability regime. We also provide results for the weighted and multi-col
In this paper, we investigate the impact of diverse user preference on learning under the stochastic multi-armed bandit (MAB) framework. We aim to show that when the user preferences are sufficiently diverse and each arm can be optimal for certain users, the O(log T) regret incurred by exploring the sub-optimal arms under the standard stochastic MAB setting can be reduced to a constant. Our intuition is that to achieve sub-linear regret, the number of times an optimal arm being pulled should scale linearly in time; when all arms are optimal for certain users and pulled frequently, the estimated arm statistics can quickly converge to their true values, thus reducing the need of exploration dramatically. We cast the problem into a stochastic linear bandits model, where both the users preferences and the state of arms are modeled as {independent and identical distributed (i.i.d)} d-dimensional random vectors. After receiving the user preference vector at the beginning of each time slot, the learner pulls an arm and receives a reward as the linear product of the preference vector and the arm state vector. We also assume that the state of the pulled arm is revealed to the learner once its pulled. We propose a Weighted Upper Confidence Bound (W-UCB) algorithm and show that it can achieve a constant regret when the user preferences are sufficiently diverse. The performance of W-UCB under general setups is also completely characterized and validated with synthetic data.
Deep learning models are considered to be state-of-the-art in many offline machine learning tasks. However, many of the techniques developed are not suitable for online learning tasks. The problem of using deep learning models with sequential data becomes even harder when several loss functions need to be considered simultaneously, as in many real-world applications. In this paper, we, therefore, propose a novel online deep learning training procedure which can be used regardless of the neural networks architecture, aiming to deal with the multiple objectives case. We demonstrate and show the effectiveness of our algorithm on the Neyman-Pearson classification problem on several benchmark datasets.
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