Assessing response quality to instructions in language models is vital but challenging due to the complexity of human language across different contexts. This complexity often results in ambiguous or inconsistent interpretations, making accurate assessment difficult. To address this issue, we propose a novel Uncertainty-aware Reward Model (URM) that introduces a robust uncertainty estimation for the quality of paired responses based on Bayesian approximation. Trained with preference datasets, our uncertainty-enabled proxy not only scores rewards for responses but also evaluates their inherent uncertainty. Empirical results demonstrate significant benefits of incorporating the proposed proxy into language model training. Our method boosts the instruction following capability of language models by refining data curation for training and improving policy optimization objectives, thereby surpassing existing methods by a large margin on benchmarks such as Vicuna and MT-bench. These findings highlight that our proposed approach substantially advances language model training and paves a new way of harnessing uncertainty within language models.

We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by N identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution, service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem using a discrete time Markov Decision Process (MDP) with a hybrid state space. We show that the optimal value function has a specific structure, which enables us to solve the hybrid MDP exactly. Moreover, we rigorously prove that as the gap between successive decision epochs grows smaller, the discrete time solution approaches the optimal solution to the original continuous time problem. To improve the scalability of our approach to a greater number of servers and task classes, we present an approximation based on state abstraction. We validate our approach on synthetic data, as well as a real financial fraud data set, which is the motivating application for this work.

We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the constraint that they may only accept at most n jobs over some reference time period. The decision-maker only has access to M independent realisations of the job arrival process. We propose an algorithm, Non-Parametric Sequential Allocation (NPSA), for solving this problem. Moreover, we prove that the expected reward returned by the NPSA algorithm converges in probability to optimality as M grows large. We demonstrate the effectiveness of the algorithm empirically on synthetic data and on public fraud-detection datasets, from where the motivation for this work is derived.

Non-cooperative cellular massive MIMO, combined with power control, is known to lead to significant improvements in per-user throughput compared with conventional LTE technology. In this paper, we investigate further refinements to massive MIMO, first, in the form of three-fold sectorization, and second, coordinated multi-point operation (with and without sectorization), in which the three base stations cooperate in the joint service of their users. For these scenarios, we analyze the downlink performance for both maximum-ratio and zero-forcing precoding and derive closed-form lower-bound expressions on the achievable rate of the users. These expressions are then used to formulate power optimization problems with two throughput fairness criteria:${i}$) network-wide max-min fairness, andii) per-cell max-min fairness. Furthermore, we provide centralized and decentralized power control strategies to optimize the transmit powers in the network. We demonstrate that employing sectorized antenna elements mitigates the detrimental effects of pilot contamination by rejecting a portion of interfering pilots in the spatial domain during channel estimation phase. Simulation results with practical sectorized antennas reveal that sectorization and multi-point coordination combined with sectorization lead to more than$1.7\times $and$2.6\times $improvements in the 95%-likely per-user throughput, respectively.

Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. Two centralized caching schemes are proposed, both of which not only utilize the user's local caches, but also exploit the correlation among the contents in the database. The first scheme implements uncoded cache placement and delivers coded contents to users using superposition coding. The second scheme, which is proposed for small cache sizes, places coded contents in users' caches and jointly encodes the cached contents of users and the messages targeted at them. The performance of the proposed schemes, which provide upper bounds on the required transmit power for a given cache capacity, is characterized. The scheme based on coded placement improves upon the first one for small cache sizes, and under certain conditions meets the uncoded placement lower bound. A lower bound on the required transmit power is also presented assuming uncoded cache placement. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussian BC can provide significant energy savings.

This paper studies the fundamental limits of content delivery in a cache-aided broadcast network for correlated content generated by a discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error-free broadcast link. A class of achievable correlation-aware schemes based on a two-step source coding approach is proposed. Library files are first compressed, and then cached and delivered using a combination of multiple-request caching schemes that are agnostic to the content correlations. The first step uses Gray-Wyner source coding to represent the library via private descriptions and descriptions that are common to more than one file. The second step then becomes a multiple-request caching problem, where the demand structure is dictated by the configuration of the compressed library, and it is interesting in its own right. The performance of the proposed two-step scheme is evaluated by comparing its achievable rate with a lower bound on the optimal peak and average rate-memory trade-offs in a two-file multiple-receiver network, and in a three-file two-receiver network. Specifically, in a network with two files and two receivers, the achievable rate matches the lower bound for a significant memory regime and it is within half of the conditional entropy of files for all other memory values. In the three-file two-receiver network, the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third one for all other cache sizes.

Caching at the wireless edge can be used to keep up with the increasing demand for high-definition wireless video streaming. By prefetching popular content into memory at wireless access points or end-user devices, requests can be served locally, relieving strain on expensive backhaul. In addition, using network coding allows the simultaneous serving of distinct cache misses via common coded multicast transmissions, resulting in significantly larger load reductions compared to those achieved with traditional delivery schemes. Most prior works simply treat video content as fixed-size files that users would like to fully download. This work is motivated by the fact that video can be coded in a scalable fashion and that the decoded video quality depends on the number of layers a user receives in sequence. Using a Gaussian source model, caching and coded delivery methods are designed to minimize the squared error distortion at end-user devices in a rate-limited caching network. The framework is very general and accounts for heterogeneous cache sizes, video popularities and user-file play-back qualities. As part of the solution, a new decentralized scheme for lossy cache-aided delivery subject to preset user distortion targets is proposed, which further generalizes prior literature to a setting with file heterogeneity.

Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. A lower bound on the required transmit power is derived, assuming uncoded cache placement, as a function of the cache capacity. A centralized joint cache and channel coding scheme is proposed, which not only utilizes the user's local caches, but also exploits the correlation among the contents in the database. This scheme provides an upper bound on the minimum required transmit power for a given cache capacity. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussian BC can provide significant energy savings.

Cache-aided coded multicast leverages side information at wireless edge caches to efficiently serve multiple unicast demands via common multicast transmissions, leading to load reductions that are proportional to the aggregate cache size. However, the increasingly dynamic, unpredictable, and personalized nature of the content that users consume challenges the efficiency of existing caching-based solutions in which only exact content reuse is explored. This paper generalizes the cache-aided coded multicast problem to specifically account for the correlation among content files, such as, for example, the one between updated versions of dynamic data. It is shown that: 1) caching content pieces based on their correlation with the rest of the library and 2) jointly compressing requested files using cached information as references during delivery, can provide load reductions that go beyond those achieved with existing schemes. This is accomplished via the design of a class of correlation-aware achievable schemes, shown to significantly outperform the state-of-the-art correlation-unaware solutions. Our results show that as we move towards real-time and/or personalized media dominated services, where exact cache hits are almost non-existent but updates can exhibit high levels of correlation, network cached information can still be useful as references for network compression.

This paper studies the fundamental limits of caching in a network with two receivers and two files generated by a two-component discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error-free broadcast link. First, a lower bound on the optimal peak rate-memory trade-off is provided. Then, in order to leverage the correlation among the library files to alleviate the load over the shared link, a two-step correlation-aware cache-aided coded multicast (CACM) scheme is proposed. The first step uses Gray-Wyner source coding to represent the library via one common and two private descriptions, such that a second correlation-unaware multiple-request CACM step can exploit the additional coded multicast opportunities that arise. It is shown that the rate achieved by the proposed two-step scheme matches the lower bound for a significant memory regime and it is within half of the conditional entropy for all other memory values.

Cache-aided coded multicast leverages side information at wireless edge caches to efficiently serve multiple groupcast demands via common multicast transmissions, leading to load reductions that are proportional to the aggregate cache size. However, the increasingly unpredictable and personalized nature of the content that users consume challenges the efficiency of existing caching-based solutions in which only exact content reuse is explored. This paper generalizes the cache-aided coded multicast problem to a source compression with distributed side information problem that specifically accounts for the correlation among the content files. It is shown how joint file compression during the caching and delivery phases can provide load reductions that go beyond those achieved with existing schemes. This is accomplished through a lower bound on the fundamental rate-memory trade-off as well as a correlation-aware achievable scheme, shown to significantly outperform state-of-the-art correlation-unaware solutions, while approaching the limiting rate-memory trade-off.