We investigate learning approximate Nash equilibrium (NE) policy profiles in two-player zero-sum imperfect information extensive-form games (IIEFGs) with last-iterate convergence guarantees. Existing algorithms either rely on full-information feedback or provide only asymptotic convergence rates. In contrast, we focus on the bandit feedback setting, where players receive feedback solely from the rewards associated with the experienced information set and action pairs in each episode. Our proposed algorithm employs a negentropy regularizer weighted by a "virtual transition" over the information set-action space to facilitate an efficient approximate policy update. Through a carefully designed virtual transition and leveraging the entropy regularization technique, we demonstrate finite-time last-iterate convergence to the NE with a rate of $\widetilde{\mathcal{O}}(k^{-\frac{1}{8}})$ under bandit feedback in each episode $k$. Empirical evaluations across various IIEFG instances show its competitive performance compared to baseline methods.

Despite significant advances in learning imperfect information extensive-form games (IIEFGs), most existing theoretical guarantees are limited to IIEFGs in the tabular case. To permit efficient learning of large-scale IIEFGs, we take the first step in studying two-player zero-sum IIEFGs with linear function approximation. In particular, we consider linear IIEFGs in the formulation of partially observable Markov games (POMGs) with linearly parameterized rewards. To address the challenge that the underlying function approximation structure is difficult to directly apply due to the imperfect information of states, we construct the composite "feature vectors" for information set-action pairs. Based on this, we further propose a "least-squares loss estimator", which we call the *fictitious* least-squares loss estimator. Through integrating this estimator with the follow-the-regularized-leader (FTRL) framework, we propose the *fictitious* least-squares follow-the-regularized-leader ($\text{F}^2\text{TRL}$) algorithm, which achieves a provable $\widetilde{\mathcal{O}}(\lambda\sqrt{d H^2 T})$ regret guarantee in the large $T$ regime, where $d$ is the ambient dimension of the feature mapping, $H$ is the horizon length, $\lambda$ is a "balance coefficient" and $T$ is the number of episodes. At the core of the analysis of $\text{F}^2\text{TRL}$ is the leverage of our proposed new "balanced transition" over information set-action space. Additionally, we complement our results with an $\Omega(\sqrt{d\min(d,H)T})$ regret lower bound for this problem and conduct empirical evaluations across various environments, which corroborate the effectiveness of our algorithm.

The linear bandit problem has been studied for many years in both stochastic and adversarial settings. Designing an algorithm that can optimize the environment without knowing the loss type attracts lots of interest. \citet{LeeLWZ021} propose an algorithm that actively detects the loss type and then switches between different algorithms specially designed for specific settings. However, such an approach requires meticulous designs to perform well in all environments. Follow-the-regularized-leader (FTRL) is another type of popular algorithm that can adapt to different environments. This algorithm is of simple design and the regret bounds are shown to be optimal in traditional multi-armed bandit problems compared with the detect-switch type. Designing an FTRL-type algorithm for linear bandits is an important question that has been open for a long time. In this paper, we prove that the FTRL algorithm with a negative entropy regularizer can achieve the best-of-three-world results for the linear bandit problem. Our regret bounds achieve the same or nearly the same order as the previous detect-switch type algorithm but with a much simpler algorithmic design.

Communication lays the foundation for cooperation in human society and in multi-agent reinforcement learning (MARL). Humans also desire to maintain their privacy when communicating with others, yet such privacy concern has not been considered in existing works in MARL. We propose the differentially private multi-agent communication (DPMAC) algorithm, which protects the sensitive information of individual agents by equipping each agent with a local message sender with rigorous (epsilon, delta)-differential privacy (DP) guarantee. In contrast to directly perturbing the messages with predefined DP noise as commonly done in privacy-preserving scenarios, we adopt a stochastic message sender for each agent respectively and incorporate the DP requirement into the sender, which automatically adjusts the learned message distribution to alleviate the instability caused by DP noise. Further, we prove the existence of a Nash equilibrium in cooperative MARL with privacy-preserving communication, which suggests that this problem is game-theoretically learnable. Extensive experiments demonstrate a clear advantage of DPMAC over baseline methods in privacy-preserving scenarios.

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.

Temporal difference (TD) learning with nonlinear function approximation (nonlinear TD learning for short) permits evaluating policies using neural networks, and is a core component in modern deep reinforcement learning. Though significant advances have been made to improve its effectiveness, little attention has been paid to the data privacy faced when applying it in real applications. To mitigate the privacy concerns in practical applications of nonlinear TD learning, in this paper, we consider preserving its privacy under the notion of differential privacy (DP). This problem is challenging since nonlinear TD learning is usually studied in the formulation of stochastic nonconvex-strongly-concave optimization to obtain finite-sample analysis, which requires simultaneously preserving privacy on both primal and dual sides. To this end, we adopt a single-timescale algorithm, which optimizes both sides using learning rates of the same order, to avoid unnecessary privacy costs. Further, we achieve a good trade-off between the privacy and utility guarantees by perturbing gradients on both sides using Gaussian noises with well-calibrated variances. Consequently, our algorithm achieves rigorous (ε,δ)-DP guarantee with the utility upper bounded by ~O((d/log(1/δ))1/8 (nε)1/4) where n is the trajectory length and d is the ambient dimension of the feature space. Extensive experiments conducted in OpenAI Gym validate the advantages of our algorithm.

Online learning to rank (OLTR) interactively learns to choose lists of items from a large collection based on certain click models that describe users' click behaviors. Most recent works for this problem focus on the stochastic environment where the item attractiveness is assumed to be invariant during the learning process. In many real-world scenarios, however, the environment could be dynamic or even arbitrarily changing. This work studies the OLTR problem in both stochastic and adversarial environments under the position-based model (PBM). We propose a method based on the follow-the-regularized-leader (FTRL) framework with Tsallis entropy and develop a new self-bounding constraint especially designed for PBM. We prove the proposed algorithm simultaneously achieves O(log T) regret in the stochastic environment and O(m√nT) regret in the adversarial environment, where T is the number of rounds, n is the number of items and m is the number of positions. We also provide a lower bound of order Ω(m√nT) for adversarial PBM, which matches our upper bound and improves over the state-of-the-art lower bound. The experiments show that our algorithm could simultaneously learn in both stochastic and adversarial environments and is competitive compared to existing methods that are designed for a single environment.

Conversational recommender systems (CRSs) have been proposed recently to mitigate the cold-start problem suffered by the traditional recommender systems. By introducing conversational key-terms, existing conversational recommenders can effectively reduce the need for extensive exploration and elicit the user preferences faster and more accurately. However, existing conversational recommenders leveraging key-terms heavily rely on the availability and quality of the key-terms, and their performances might degrade significantly when the key-terms are incomplete or not well labeled, which usually happens when there are new items being consistently incorporated into the systems and involving lots of human efforts to acquire well-labeled key-terms is costly. Besides, existing CRS methods leverage the feedback to different conversational key-terms separately, without considering the underlying relations between the key-terms. In this case, the learning of the conversational recommenders is sample inefficient, especially when there is a large number of candidate conversational key-terms.

Conversational recommender systems elicit user preference via interactive conversational interactions. By introducing conversational key-terms, existing conversational recommenders can effectively reduce the need for extensive exploration in a traditional interactive recommender. However, there are still limitations of existing conversational recommender approaches eliciting user preference via key-terms. First, the key-term data of the items needs to be carefully labeled, which requires a lot of human efforts. Second, the number of the human labeled key-terms is limited and the granularity of the key-terms is fixed, while the elicited user preference is usually from coarse-grained to fine-grained during the conversations. In this paper, we propose a clustering of conversational bandits algorithm. To avoid the human labeling efforts and automatically learn the key-terms with the proper granularity, we online cluster the items and generate meaningful key-terms for the items during the conversational interactions. Our algorithm is general and can also be used in the user clustering when the feedback from multiple users is available, which further leads to more accurate learning and generations of conversational key-terms. We analyze the regret bound of our learning algorithm. In the empirical evaluations, without using any human labeled key-terms, our algorithm effectively generates meaningful coarse-to-fine grained key-terms and performs as well as or better than the state-of-the-art baseline.

With the recent advances of conversational recommendations, the recommender system is able to actively and dynamically elicit user preference via conversational interactions. To achieve this, the system periodically queries users' preference on attributes and collects their feedback. However, most existing conversational recommender systems only enable the user to provide absolute feedback to the attributes. In practice, the absolute feedback is usually limited, as the users tend to provide biased feedback when expressing the preference. Instead, the user is often more inclined to express comparative preferences, since user preferences are inherently relative. To enable users to provide comparative preferences during conversational interactions, we propose a novel comparison-based conversational recommender system. The relative feedback, though more practical, is not easy to be incorporated since its feedback scale is always mismatched with users' absolute preferences. With effectively collecting and understanding the relative feedback from an interactive manner, we further propose a new bandit algorithm, which we call RelativeConUCB. The experiments on both synthetic and real-world datasets validate the advantage of our proposed method, compared to the existing bandit algorithms in the conversational recommender systems.