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In this paper, we study Lipschitz bandit problems with batched feedback, where the expected reward is Lipschitz and the reward observations are communicated to the player in batches. We introduce a novel landscape-aware algorithm, called Batched Lipschitz Narrowing (BLiN), that optimally solves this problem. Specifically, we show that for a $T$-step problem with Lipschitz reward of zooming dimension $d_z$, our algorithm achieves theoretically optimal regret rate of $ \widetilde{\mathcal{O}} \left( T^{\frac{d_z + 1}{d_z + 2}} \right) $ using only $ \mathcal{O} \left( \log\log T\right) $ batches. We also provide complexity analysis for this problem. Our theoretical lower bound implies that $\widetilde{\Omega}(\log\log T)$ batches are necessary for any algorithm to achieve the optimal regret. Thus, up to logarithmic factors, BLiN achieves optimal regret rate using minimal communication.

We consider the fixed-budget best arm identification problem in two-armed Gaussian bandits with unknown variances. The tightest lower bound on the complexity and an algorithm whose performance guarantee matches the lower bound have long been open problems when the variances are unknown and when the algorithm is agnostic to the optimal proportion of the arm draws. In this paper, we propose a strategy comprising a sampling rule with randomized sampling (RS) following the estimated target allocation probabilities of arm draws and a recommendation rule using the augmented inverse probability weighting (AIPW) estimator, which is often used in the causal inference literature. We refer to our strategy as the RS-AIPW strategy. In the theoretical analysis, we first derive a large deviation principle for martingales, which can be used when the second moment converges in mean, and apply it to our proposed strategy. Then, we show that the proposed strategy is asymptotically optimal in the sense that the probability of misidentification achieves the lower bound by Kaufmann et al. (2016) when the sample size becomes infinitely large and the gap between the two arms goes to zero.

Prescribing optimal operation based on the condition of the system and, thereby, potentially prolonging the remaining useful lifetime has a large potential for actively managing the availability, maintenance and costs of complex systems. Reinforcement learning (RL) algorithms are particularly suitable for this type of problems given their learning capabilities. A special case of a prescriptive operation is the power allocation task, which can be considered as a sequential allocation problem, where the action space is bounded by a simplex constraint. A general continuous action-space solution of such sequential allocation problems has still remained an open research question for RL algorithms. In continuous action-space, the standard Gaussian policy applied in reinforcement learning does not support simplex constraints, while the Gaussian-softmax policy introduces a bias during training. In this work, we propose the Dirichlet policy for continuous allocation tasks and analyze the bias and variance of its policy gradients. We demonstrate that the Dirichlet policy is bias-free and provides significantly faster convergence, better performance and better hyperparameters robustness over the Gaussian-softmax policy. Moreover, we demonstrate the applicability of the proposed algorithm on a prescriptive operation case, where we propose the Dirichlet power allocation policy and evaluate the performance on a case study of a set of multiple lithium-ion (Li-I) battery systems. The experimental results show the potential to prescribe optimal operation, improve the efficiency and sustainability of multi-power source systems.

We consider the dynamic pricing problem with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is jointly determined by the price and an observable covariate vector $x_t\in\mathbb{R}^d$ through an unknown generalized linear model. Most of the existing literature assumes the covariate vectors $x_t$'s are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper we show that a simple pricing algorithm has an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$ (which can even be arbitrarily chosen). The upper bound on the regret matches the lower bound (even under the i.i.d. assumption) up to logarithmic factors. Our paper thus shows that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the $x_t$'s, a quantity present in previous bounds. Furthermore, we discuss a condition under which a better regret is achievable and how a Thompson sampling algorithm can be applied to give an efficient computation of the prices.

Logistic Bandits have recently undergone careful scrutiny by virtue of their combined theoretical and practical relevance. This research effort delivered statistically efficient algorithms, improving the regret of previous strategies by exponentially large factors. Such algorithms are however strikingly costly as they require $\Omega(t)$ operations at each round. On the other hand, a different line of research focused on computational efficiency ($\mathcal{O}(1)$ per-round cost), but at the cost of letting go of the aforementioned exponential improvements. Obtaining the best of both world is unfortunately not a matter of marrying both approaches. Instead we introduce a new learning procedure for Logistic Bandits. It yields confidence sets which sufficient statistics can be easily maintained online without sacrificing statistical tightness. Combined with efficient planning mechanisms we design fast algorithms which regret performance still match the problem-dependent lower-bound of Abeille et al. (2021). To the best of our knowledge, those are the first Logistic Bandit algorithms that simultaneously enjoy statistical and computational efficiency.

We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data, determining the unknown state and action parameters, and performing sensitivity analysis with respect to problem parameters. We consider two broad categories of sequential decision making problems modelled as infinite horizon Markov Decision Processes (MDPs) with (and without) an absorbing state. The central idea underlying our framework is to quantify exploration in terms of the Shannon Entropy of the trajectories under the MDP and determine the stochastic policy that maximizes it while guaranteeing a low value of the expected cost along a trajectory. This resulting policy enhances the quality of exploration early on in the learning process, and consequently allows faster convergence rates and robust solutions even in the presence of noisy data as demonstrated in our comparisons to popular algorithms such as Q-learning, Double Q-learning and entropy regularized Soft Q-learning. The framework extends to the class of parameterized MDP and RL problems, where states and actions are parameter dependent, and the objective is to determine the optimal parameters along with the corresponding optimal policy. Here, the associated cost function can possibly be non-convex with multiple poor local minima. Simulation results applied to a 5G small cell network problem demonstrate successful determination of communication routes and the small cell locations. We also obtain sensitivity measures to problem parameters and robustness to noisy environment data.

User dissatisfaction due to buffering pauses during streaming is a significant cost to the system, which we model as a non-decreasing function of the frequency of buffering pause. Minimization of total user dissatisfaction in a multi-channel cellular network leads to a non-convex problem. Utilizing a combinatorial structure in this problem, we first propose a polynomial time joint admission control and channel allocation algorithm which is provably (almost) optimal. This scheme assumes that the base station (BS) knows the frame statistics of the streams. In a more practical setting, where these statistics are not available a priori at the BS, a learning based scheme with provable guarantees is developed. This learning based scheme has relation to regret minimization in multi-armed bandits with non-i.i.d. and delayed reward (cost). All these algorithms require none to minimal feedback from the user equipment to the base station regarding the states of the media player buffer at the application layer, and hence, are of practical interest.

Recently, deep multiagent reinforcement learning (MARL) has become a highly active research area as many real-world problems can be inherently viewed as multiagent systems. A particularly interesting and widely applicable class of problems is the partially observable cooperative multiagent setting, in which a team of agents learns to coordinate their behaviors conditioning on their private observations and commonly shared global reward signals. One natural solution is to resort to the centralized training and decentralized execution paradigm. During centralized training, one key challenge is the multiagent credit assignment: how to allocate the global rewards for individual agent policies for better coordination towards maximizing system-level's benefits. In this paper, we propose a new method called Q-value Path Decomposition (QPD) to decompose the system's global Q-values into individual agents' Q-values. Unlike previous works which restrict the representation relation of the individual Q-values and the global one, we leverage the integrated gradient attribution technique into deep MARL to directly decompose global Q-values along trajectory paths to assign credits for agents. We evaluate QPD on the challenging StarCraft II micromanagement tasks and show that QPD achieves the state-of-the-art performance in both homogeneous and heterogeneous multiagent scenarios compared with existing cooperative MARL algorithms.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.