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1. Second Order Path Variationals in Non-Stationary Online Learning

   Baby, Dheeraj and ; Wang, Yu-Xiang ( April 2023 , Proceedings of Machine Learning Research)

   Ruiz, Francisco and (Ed.)

   We consider the problem of universal dynamic regret minimization under exp-concave and smooth losses. We show that appropriately designed Strongly Adaptive algorithms achieve a dynamic regret of $\tilde O(d^2 n^{1/5} [\mathcal{TV}_1(w_{1:n})]^{2/5} \vee d^2)$, where $n$ is the time horizon and $\mathcal{TV}_1(w_{1:n})$ a path variational based on second order differences of the comparator sequence. Such a path variational naturally encodes comparator sequences that are piece-wise linear – a powerful family that tracks a variety of non-stationarity patterns in practice (Kim et al., 2009). The aforementioned dynamic regret is shown to be optimal modulo dimension dependencies and poly-logarithmic factors of $n$. To the best of our knowledge, this path variational has not been studied in the non-stochastic online learning literature before. Our proof techniques rely on analysing the KKT conditions of the offline oracle and requires several non-trivial generalizations of the ideas in Baby and Wang (2021) where the latter work only implies an $\tilde{O}(n^{1/3})$ regret for the current problem. 

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2. Adaptive Online Estimation of Piecewise Polynomial Trends

   Baby, Dheeraj ; Wang, Yu-Xiang ( December 2020 , NeurIPS 2020)

   null (Ed.)

   We consider the framework of non-stationary stochastic optimization (Besbes et al., 2015) with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is studied. Motivated from the theory of non-parametric regression, we introduce a new variational constraint that enforces the comparator sequence to belong to a discrete k^{th} order Total Variation ball of radius C_n. This variational constraint models comparators that have piece-wise polynomial structure which has many relevant practical applications (Tibshirani, 2014). By establishing connections to the theory of wavelet based non-parametric regression, we design a polynomial time algorithm that achieves the nearly optimal dynamic regret of ~O(n^{1/(2k+3)} C_n^{2/(2k+3)}). The proposed policy is adaptive to the unknown radius C_n. Further, we show that the same policy is minimax optimal for several other non-parametric families of interest. 

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3. Dynamic Regret of Policy Optimization in Non-Stationary Environments

   Fei, Yingjie ; Yang, Zhuoran ; Wang, Zhaoran ; Xie, Qiaomin ( December 2020 , Advances in neural information processing systems)

   null (Ed.)

   We consider reinforcement learning (RL) in episodic MDPs with adversarial full-information reward feedback and unknown fixed transition kernels. We propose two model-free policy optimization algorithms, POWER and POWER++, and establish guarantees for their dynamic regret. Compared with the classical notion of static regret, dynamic regret is a stronger notion as it explicitly accounts for the non-stationarity of environments. The dynamic regret attained by the proposed algorithms interpolates between different regimes of non-stationarity, and moreover satisfies a notion of adaptive (near-)optimality, in the sense that it matches the (near-)optimal static regret under slow-changing environments. The dynamic regret bound features two components, one arising from exploration, which deals with the uncertainty of transition kernels, and the other arising from adaptation, which deals with non-stationary environments. Specifically, we show that POWER++ improves over POWER on the second component of the dynamic regret by actively adapting to non-stationarity through prediction. To the best of our knowledge, our work is the first dynamic regret analysis of model-free RL algorithms in non-stationary environments. 

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4. Dynamic Environment Responsive Online Meta-Learning with Fairness Awareness

   https://doi.org/10.1145/3648684  

   Zhao, Chen ; Mi, Feng ; Wu, Xintao ; Jiang, Kai ; Khan, Latifur ; Chen, Feng ( July 2024 , ACM Transactions on Knowledge Discovery from Data)

   The fairness-aware online learning framework has emerged as a potent tool within the context of continuous lifelong learning. In this scenario, the learner’s objective is to progressively acquire new tasks as they arrive over time, while also guaranteeing statistical parity among various protected sub-populations, such as race and gender when it comes to the newly introduced tasks. A significant limitation of current approaches lies in their heavy reliance on the i.i.d (independent and identically distributed) assumption concerning data, leading to a static regret analysis of the framework. Nevertheless, it’s crucial to note that achieving low static regret does not necessarily translate to strong performance in dynamic environments characterized by tasks sampled from diverse distributions. In this article, to tackle the fairness-aware online learning challenge in evolving settings, we introduce a unique regret measure, FairSAR, by incorporating long-term fairness constraints into a strongly adapted loss regret framework. Moreover, to determine an optimal model parameter at each time step, we introduce an innovative adaptive fairness-aware online meta-learning algorithm, referred to as FairSAOML. This algorithm possesses the ability to adjust to dynamic environments by effectively managing bias control and model accuracy. The problem is framed as a bi-level convex-concave optimization, considering both the model’s primal and dual parameters, which pertain to its accuracy and fairness attributes, respectively. Theoretical analysis yields sub-linear upper bounds for both loss regret and the cumulative violation of fairness constraints. Our experimental evaluation of various real-world datasets in dynamic environments demonstrates that our proposed FairSAOML algorithm consistently outperforms alternative approaches rooted in the most advanced prior online learning methods.

    

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5. Implicit Parameter-free Online Learning with Truncated Linear Models

   Chen, Keyi ; Cutkosky, Ashok ; Orabona, Francesco ( January 2022 , International Conference on Algorithmic Learning Theory)

   Dasgupta, Sanjoy ; Haghtalab, Nika (Ed.)

   Parameter-free algorithms are online learning algorithms that do not require setting learning rates. They achieve optimal regret with respect to the distance between the initial point and any competitor. Yet, parameter-free algorithms do not take into account the geometry of the losses. Recently, in the stochastic optimization literature, it has been proposed to instead use truncated linear lower bounds, which produce better performance by more closely modeling the losses. In particular, truncated linear models greatly reduce the problem of overshooting the minimum of the loss function. Unfortunately, truncated linear models cannot be used with parameter-free algorithms because the updates become very expensive to compute. In this paper, we propose new parameter-free algorithms that can take advantage of truncated linear models through a new update that has an “implicit” flavor. Based on a novel decomposition of the regret, the new update is efficient, requires only one gradient at each step, never overshoots the minimum of the truncated model, and retains the favorable parameter-free properties. We also conduct an empirical study demonstrating the practical utility of our algorithms. 

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