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Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Yu-Jie Zhang, Masashi Sugiyama

This paper investigates the logistic bandit problem, a variant of the generalized linear bandit model that utilizes a logistic model to depict the feedback from an action. While most existing research focuses on the binary logistic bandit problem, the multinomial case, which considers more than two possible feedback values, offers increased practical relevance and adaptability for use in complex decision-making problems such as reinforcement learning. In this paper, we provide an algorithm that enjoys both statistical and computational efficiency for the logistic bandit problem. In the binary case, our method improves the state-of-the-art binary logistic bandit method by reducing the per-round computation cost from $\mathcal{O}(\log T)$ to $\mathcal{O}(1)$ with respect to the time horizon $T$, while still preserving the minimax optimal guarantee up to logarithmic factors. In the multinomial case, with $K+1$ potential feedback values, our algorithm achieves an $\tilde{\mathcal{O}}(K\sqrt{T})$ regret bound with $\mathcal{O}(1)$ computational cost per round. The result not only improves the $\tilde{\mathcal{O}}(K\sqrt{\kappa T})$ bound for the best-known tractable algorithm—where the large constant $\kappa$ increases exponentially with the diameter of the parameter domain—but also reduces the $\mathcal{O}(T)$ computational complexity demanded by the previous method.

Reinforcement Learning/Online

Canzhe Zhao, Ruofeng Yang, Baoxiang Wang, Xuezhou Zhang, Shuai Li

In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to the learner at the end of each episode. We propose a policy optimization-based algorithm POLO, and we prove that it attains the $\widetilde{O}(K^{\frac{5}{6}}A^{\frac{1}{2}}d\ln(1+M)/(1-\gamma)^2)$ regret guarantee, where $d$ is rank of the transition kernel (and hence the dimension of the unknown representations), $A$ is the cardinality of the action space, $M$ is the cardinality of the model class that contains all the plausible representations, and $\gamma$ is the discounted factor. Notably, our algorithm is oracle-efficient and has a regret guarantee with no dependence on the size of potentially arbitrarily large state space. Furthermore, we also prove an $\Omega(\frac{\gamma^2}{1-\gamma} \sqrt{d A K})$ regret lower bound for this problem, showing that low-rank MDPs are statistically more difficult to learn than linear MDPs in the regret minimization setting. To the best of our knowledge, we present the first algorithm that interleaves representation learning, exploration, and exploitation to achieve the sublinear regret guarantee for RL with nonlinear function approximation and adversarial losses.

Reinforcement Learning/Online

Hai Zhang, Hang Yu, Junqiao Zhao, Di Zhang, xiao zhang, Hongtu Zhou, Chang Huang, Chen Ye

Designing and deriving effective model-based reinforcement learning (MBRL) algorithms with a performance improvement guarantee is challenging, mainly attributed to the high coupling between model learning and policy optimization. Many prior methods that rely on return discrepancy to guide model learning ignore the impacts of model shift, which can lead to performance deterioration due to excessive model updates. Other methods use performance difference bound to explicitly consider model shift. However, these methods rely on a fixed threshold to constrain model shift, resulting in a heavy dependence on the threshold and a lack of adaptability during the training process. In this paper, we theoretically derive an optimization objective that can unify model shift and model bias and then formulate a fine-tuning process. This process adaptively adjusts the model updates to get a performance improvement guarantee while avoiding model overfitting. Based on these, we develop a straightforward algorithm USB-PO (Unified model Shift and model Bias Policy Optimization). Empirical results show that USB-PO achieves state-of-the-art performance on several challenging benchmark tasks.

Reinforcement Learning/Online

Lucas N. Alegre, Ana Bazzan, Ann Nowe, Bruno C. da Silva

We introduce a principled method for performing zero-shot transfer in reinforcement learning (RL) by exploiting approximate models of the environment. Zero-shot transfer in RL has been investigated by leveraging methods rooted in generalized policy improvement (GPI) and successor features (SFs). Although computationally efficient, these methods are model-free: they analyze a library of policies---each solving a particular task---and identify which action the agent should take. We investigate the more general setting where, in addition to a library of policies, the agent has access to an approximate environment model. Even though model-based RL algorithms can identify near-optimal policies, they are typically computationally intensive. We introduce $h$-GPI, a multi-step extension of GPI that interpolates between these extremes---standard model-free GPI and fully model-based planning---as a function of a parameter, $h$, regulating the amount of time the agent has to reason. We prove that $h$-GPI's performance lower bound is strictly better than GPI's, and show that $h$-GPI generally outperforms GPI as $h$ increases. Furthermore, we prove that as $h$ increases, $h$-GPI's performance becomes arbitrarily less susceptible to sub-optimality in the agent's policy library. Finally, we introduce novel bounds characterizing the gains achievable by $h$-GPI as a function of approximation errors in both the agent's policy library and its (possibly learned) model. These bounds strictly generalize those known in the literature. We evaluate $h$-GPI on challenging tabular and continuous-state problems under value function approximation and show that it consistently outperforms GPI and state-of-the-art competing methods under various levels of approximation errors.

Reinforcement Learning/Online

Long-Fei Li, Peng Zhao, Zhi-Hua Zhou

We study reinforcement learning in episodic inhomogeneous MDPs with adversarial full-information rewards and the unknown transition kernel. We consider the linear mixture MDPs whose transition kernel is a linear mixture model and choose the \emph{dynamic regret} as the performance measure. Denote by $d$ the dimension of the feature mapping, $H$ the horizon, $K$ the number of episodes, $P_T$ the non-stationary measure, we propose a novel algorithm that enjoys an $\widetilde{\mathcal{O}}\big(\sqrt{d^2 H^3K} + \sqrt{H^4(K+P_T)(1+P_T)}\big)$ dynamic regret under the condition that $P_T$ is known, which improves previously best-known dynamic regret for adversarial linear mixture MDP and adversarial tabular MDPs. We also establish an $\Omega\big(\sqrt{d^2 H^3 K} + \sqrt{H K (H+P_T)}\big)$ lower bound, indicating our algorithm is \emph{optimal} in $K$ and $P_T$. Furthermore, when the non-stationary measure $P_T$ is unknown, we design an online ensemble algorithm with a meta-base structure, which is proved to achieve an $\widetilde{\mathcal{O}}\big(\sqrt{d^2 H^3K} + \sqrt{H^4(K+P_T)(1+P_T) + H^2 S_T^2}\big)$ dynamic regret and here $S_T$ is the expected switching number of the best base-learner. The result can be optimal under certain regimes.