The advent of Cellular Vehicle-to-Everything (CV2X) technology has revolutionised intelligent transportation systems (ITS), but poses challenges for secure and efficient data sharing due to its dynamic nature. Traditional centralised systems are inadequate, prompting the need for decentralised solutions like blockchain. However, applying blockchain technologies in C-V2X always faces scalability issues. This paper proposes a scalable C-V2X blockchain network with a hierarchical consensus by integrating a dynamic load-balancing sharding mechanism and zero-knowledge proofs (ZKPs). Our scheme ensures scalability in the C-V2X environment through sharding while utilising ZKPs to enhance cross-shard validation efficiency, reducing its complexity to$O(1)$. Additionally, our approach reduces bandwidth consumption by 90.8% compared to Merkle tree-based solutions and its consensus time is lower than 360 ms.

We consider a decision maker allocating one unit of renewable and divisible resource in each period on a number of arms. The arms have unknown and random rewards whose means are proportional to the allocated resource and whose variances are proportional to an order $b$ of the allocated resource. When the order ranges from 0 to 1, the framework smoothly bridges the standard stochastic multi-armed bandit and online learning with full feedback. We design two algorithms that attain the optimal gap-dependent and gap-independent regret bounds for $b\in [0,1]$, and demonstrate a phase transition at $b=1/2$. The theoretical results hinge on a novel concentration inequality we have developed that bounds a linear combination of sub-Gaussian random variables whose weights are fractional, adapted to the filtration, and monotonic.

We consider a contextual online learning (multi-armed bandit) problem with high-dimensional covariate $x$ and decision $y$. The reward function to learn, $f(x,y)$, does not have a particular parametric form. The literature has shown that the optimal regret is $\tilde{O}(T^{(d_x\!+\!d_y\!+\!1)/(d_x\!+\!d_y\!+\!2)})$, where $d_x$ and $d_y$ are the dimensions of $x$ and $y$, and thus it suffers from the curse of dimensionality. In many applications, only a small subset of variables in the covariate affect the value of $f$, which is referred to as sparsity in statistics. To take advantage of the sparsity structure of the covariate, we propose a variable selection algorithm called BV-LASSO, which incorporates novel ideas such as binning and voting to apply LASSO to nonparametric settings. Using it as a subroutine, we can achieve the regret $\tilde{O}(T^{(d_x^*\!+\!d_y\!+\!1)/(d_x^*\!+\!d_y\!+\!2)})$, where $d_x^*$ is the effective covariate dimension. The regret matches the optimal regret when the covariate is $d^*_x$-dimensional and thus cannot be improved. Our algorithm may serve as a general recipe to achieve dimension reduction via variable selection in nonparametric settings.

It has been recently shown in the literature (Nie et al, 2018; Shin et al, 2019a,b) that the sample averages from online learning experiments are biased when used to estimate the mean reward. To correct the bias, off-policy evaluation methods, including importance sampling and doubly robust estimators, typically calculate the conditional propensity score, which is ill-defined for non-randomized policies such as UCB. This paper provides a procedure to debias the samples using bootstrap, which doesn’t require the knowledge of the reward distribution and can be applied to any adaptive policies. Numerical experiments demonstrate the effective bias reduction for samples generated by popular multi-armed bandit algorithms such as Explore-Then-Commit (ETC), UCB, Thompson sampling (TS) and $\epsilon$-greedy (EG). We analyze and provide theoretical justifications for the procedure under the ETC algorithm, including the asymptotic convergence of the bias decay rate in the real and bootstrap worlds.

In many online learning or multi-armed bandit problems, the taken actions or pulled arms are ordinal and required to be monotone over time. Examples include dynamic pricing, in which the firms use markup pricing policies to please early adopters and deter strategic waiting, and clinical trials, in which the dose allocation usually follows the dose escalation principle to prevent dose limiting toxicities. We consider the continuum-armed bandit problem when the arm sequence is required to be monotone. We show that when the unknown objective function is Lipschitz continuous, the regret is $O(T)$. When in addition the objective function is unimodal or quasiconcave, the regret is $\tilde O(T^{3/4})$ under the proposed algorithm, which is also shown to be the optimal rate. This deviates from the optimal rate $\tilde O(T^{2/3})$ in the continuous-armed bandit literature and demonstrates the cost to the learning efficiency brought by the monotonicity requirement.

We study a multi-armed bandit problem where the rewards exhibit regime switching. Specifically, the distributions of the random rewards generated from all arms are modulated by a common underlying state modeled as a finite-state Markov chain. The agent does not observe the underlying state and has to learn the transition matrix and the reward distributions. We propose a learning algorithm for this problem, building on spectral method-of-moments estimations for hidden Markov models, belief error control in partially observable Markov decision processes and upper-confidence-bound methods for online learning. We also establish an upper bound $O(T^{2/3}\sqrt{\log T})$ for the proposed learning algorithm where $T$ is the learning horizon. Finally, we conduct proof-of-concept experiments to illustrate the performance of the learning algorithm.

Online retailing has seen steady growth over the last decade. According to the Digital Commerce (formerly Internet Retailer) analysis of the US Commerce Department's year-end retail data, online sales constituted 16% of all retail sales in 2019, and is forecast to reach higher levels in the next years due to the impact of COVID-19. For an online retailer, one of the most important decisions is the products' display positioning as it plays a crucial role in shaping customers' shopping behavior. Empirical evidence abounds. Baye et al. [2] find that a consumer's likelihood of purchasing from a firm is strongly related to the order in which the firm is listed on a webpage by a search engine. In the online advertising industry, it has been widely observed that ads placed higher on a webpage attract more clicks from consumers [1]. Given the importance of product ranking positions, the key question for online retailers is how to rank the products to maximize the revenue.

In the online video game industry, a significant portion of the revenue is generated from microtransactions, where a small amount of real-world currency is exchanged for virtual items to be used in the game. One popular way to conduct microtransactions is via a loot box, which is a random bundle of virtual items whose contents are not revealed until after purchase. In this work, we consider how to optimally price and design loot boxes from the perspective of a revenue-maximizing video game company, and analyze customer surplus under such selling strategies. Our paper provides the first formal treatment of loot boxes, with the aim to provide customers, companies, and regulatory bodies with insights into this popular selling strategy. We consider two types of loot boxes: a traditional one where customers can receive (unwanted) duplicates, and a unique one where customers are guaranteed to never receive duplicates. We show that as the number of virtual items grows large, the unique box strategy is asymptotically optimal, while the traditional box strategy only garners 36.7% of the optimal revenue. On the other hand, unique box strategies leaves almost zero customer surplus, while traditional box strategies leaves positive surplus. Further, when designing traditional and unique loot boxes, we show it is asymptotically optimal to allocate the items uniformly, even when the item valuation distributions are highly heterogeneous. We also show that when the seller purposely misrepresents the allocation probabilities, then their revenue may increase significantly and thus strict regulation is needed. Finally, we show that even if the seller allows customers to salvage unwanted items, then the customer surplus can only increase by at most 1.4%.