The multiaccess coded caching (MACC) system, as formulated by Hachem {\it et al.}, consists of a central server with a library of $N$ files, connected to $K$ cache-less users via an error-free shared link, and $K$ cache nodes, each equipped with cache memory of size $M$ files. Each user can access $L$ neighboring cache nodes under a cyclic wrap-around topology. Most existing studies operate under the strong assumption that users can retrieve content from their connected cache nodes at no communication cost. In practice, each user retrieves content from its $L$ different connected cache nodes at varying costs. Additionally, the server also incurs certain costs to transmit the content to the users. In this paper, we focus on a cost-aware MACC system and aim to minimize the total system cost, which includes cache-access costs and broadcast costs. Firstly, we propose a novel coded caching framework based on superposition coding, where the MACC schemes of Cheng \textit{et al.} are layered. Then, a cost-aware optimization problem is derived that optimizes cache placement and minimizes system cost. By identifying a sparsity property of the optimal solution, we propose a structure-aware al
In the classic sequential testing problem, we are given a system with several components each of which fails with some independent probability. The goal is to identify whether or not some component has failed. When the test costs are additive, it is well known that a greedy algorithm finds an optimal solution. We consider a much more general setting with subadditive cost functions and provide a $(4ρ+γ)$-approximation algorithm, assuming a $γ$-approximate value oracle (that computes the cost of any subset) and a $ρ$-approximate ratio oracle (that finds a subset with minimum ratio of cost to failure probability). While the natural greedy algorithm has a poor approximation ratio in the subadditive case, we show that a suitable truncation achieves the above guarantee. Our analysis is based on a connection to the minimum sum set cover problem. As applications, we obtain the first approximation algorithms for sequential testing under various cost-structures: $(5+ε)$-approximation for tree-based costs, $9.5$-approximation for routing costs and $(4+\ln n)$ for machine activation costs. We also show that sequential testing under submodular costs does not admit any poly-logarithmic approxima
In the online general knapsack problem, an algorithm is presented with an item $x=(s,v)$ of size $s$ and value $v$ and must irrevocably choose to pack such an item into the knapsack or reject it before the next item appears. The goal is to maximize the total value of the packed items without overflowing the knapsack's capacity. As this classical setting is way too harsh for many real-life applications, we will analyze the online general knapsack problem under the reservation model. Here, instead of accepting or rejecting an item immediately, an algorithm can delay the decision of whether to pack the item by paying a fraction $0\le α$ of the size or the value of the item. This models many practical applications, where, for example, decisions can be delayed for some costs e.g. cancellation fees. We present results for both variants: First, for costs depending on the size of the items and then for costs depending on the value of the items. If the reservation costs depend on the size of the items, we find a matching upper and lower bound of $2$ for every $α$. On the other hand, if the reservation costs depend on the value of the items, we find that no algorithm is competitive for reser
Generative AI and LLMs in particular are heavily used nowadays for various document processing tasks such as question answering and summarization. However, different LLMs come with different capabilities for different tasks as well as with different costs, tokenization, and latency. In fact, enterprises are already incurring huge costs of operating or using LLMs for their respective use cases. In this work, we propose optimizing the usage costs of LLMs by estimating their output quality (without actually invoking the LLMs), and then solving an optimization routine for the LLM selection to either keep costs under a budget, or minimize the costs, in a quality and latency aware manner. We propose a model to predict the output quality of LLMs on document processing tasks like summarization, followed by an LP rounding algorithm to optimize the selection of LLMs. We study optimization problems trading off the quality and costs, both theoretically and empirically. We further propose a sentence simplification model for reducing the number of tokens in a controlled manner. Additionally, we propose several deterministic heuristics for reducing tokens in a quality aware manner, and study the
In international trade, firms face lengthy ordering-producing-delivery times and make shipping frequency decisions based on the per-shipment costs and financing costs. In this paper, I develop a model of importer-exporter procurement where the importer procures international inputs from exporting firms in developing countries. The exporters are credit constrained for working capital, incur the per-shipment fixed costs, and get paid after goods are delivered to the importer. The model shows that the shipping frequency increases for high financing costs in origin and destination. Furthermore, longer delivery times increase shipping frequency as well as procurement costs. The model also shows that the higher per-shipment fixed costs reduce the shipping frequency, in line with previous literature. Reduced transaction costs lower the exporter's demand for financial services through shipping frequency adjustment, mitigating the financial frictions of the firm. Then, I empirically investigate whether the conclusions regarding the effect of per-shipment fixed costs on shipping frequency from the theoretical model and in the existing literature extend to developing countries. My estimation
We study voluntary disclosure with multiple biased senders who may bear costs for disclosing or concealing their private information. Under relevant assumptions, disclosures are strategic substitutes under a disclosure cost but complements under a concealment cost. Additional senders thus impede any sender's disclosure under a disclosure cost but promote it under a concealment cost. In the former case, a decision maker can be harmed by additional senders, even when senders have opposing interests. The effects under both kinds of message costs turn on how a sender, when concealing his information, expects others' messages to systematically sway the decision maker's belief.
This paper studies a generalized variant of the Colonel Blotto game, referred to as the Colonel Blotto game with costs. Unlike the classic Colonel Blotto game, which imposes the use-it-or-lose-it budget assumption, the Colonel Blotto game with costs captures the strategic importance of costs related both to obtaining resources and assigning them across battlefields. We show that every instance of the Colonel Blotto game with costs is strategically equivalent to an instance of the zero-sum Colonel Blotto game with one additional battlefield. This enables the computation of Nash equilibria of the Colonel Blotto game with costs in polynomial time with respect to the game parameters: the number of battlefields and the number of resources available to the players.
The costs of training frontier AI models have grown dramatically in recent years, but there is limited public data on the magnitude and growth of these expenses. This paper develops a detailed cost model to address this gap, estimating training costs using three approaches that account for hardware, energy, cloud rental, and staff expenses. The analysis reveals that the amortized cost to train the most compute-intensive models has grown precipitously at a rate of 2.4x per year since 2016 (90% CI: 2.0x to 2.9x). For key frontier models, such as GPT-4 and Gemini, the most significant expenses are AI accelerator chips and staff costs, each costing tens of millions of dollars. Other notable costs include server components (15-22%), cluster-level interconnect (9-13%), and energy consumption (2-6%). If the trend of growing development costs continues, the largest training runs will cost more than a billion dollars by 2027, meaning that only the most well-funded organizations will be able to finance frontier AI models.
We study a variant of cost-aware sequential hypothesis testing in which a single active Decision Maker (DM) selects actions with positive, random costs to identify the true hypothesis under an average error constraint, while minimizing the expected total cost. The DM may abort an in-progress action, yielding no sample, by truncating its realized cost at a smaller, tunable deterministic limit, which we term a per-action deadline. We analyze how this cancellation option can be exploited under two cost-revelation models: ex-post, where the cost is revealed only after the sample is obtained, and ex-ante, where the cost accrues before sample acquisition. In the ex-post model, per-action deadlines do not affect the expected total cost, and the cost-error tradeoffs coincide with the baseline obtained by replacing deterministic costs with cost means. In the ex-ante model, we show how per-action deadlines inflate the expected number of times actions are applied, and that the resulting expected total cost can be reduced to the constant-cost setting by introducing an effective per-action cost. We characterize when deadlines are beneficial and study several families in detail.
Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many real-world scenarios, controlling certain query variables may incur costs. Therefore, the learner needs to balance the selection of informative subsets for targeted learning against leaving some variables to be randomly sampled to minimize costs. This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS). While the goal of BOCVS is to identify the optimal solution with minimal cost, previous works have only guaranteed finding the optimal solution without considering the total costs incurred. Moreover, these works assume precise knowledge of the cost for each subset, which is often unrealistic. In this paper, we propose a novel algorithm for the extension of the BOCVS problem with random and unknown costs that separates the process into exploration and exploitation phases. The exploration phase will filter out low-quality variable subsets, while the exploitation phase will leverage high-quality ones. Furthermore, we
We study the costs of coal-fired electricity in the United States between 1882 and 2006 by decomposing it in terms of the price of coal, transportation costs, energy density, thermal efficiency, plant construction cost, interest rate, capacity factor, and operations and maintenance cost. The dominant determinants of costs have been the price of coal and plant construction cost. The price of coal appears to fluctuate more or less randomly while the construction cost follows long-term trends, decreasing from 1902 - 1970, increasing from 1970 - 1990, and leveling off since then. Our analysis emphasizes the importance of using long time series and comparing electricity generation technologies using decomposed total costs, rather than costs of single components like capital. By taking this approach we find that the history of coal-fired electricity costs suggests there is a fluctuating floor to its future costs, which is determined by coal prices. Even if construction costs resumed a decreasing trend, the cost of coal-based electricity would drop for a while but eventually be determined by the price of coal, which fluctuates while showing no long-term trend.
We study service scheduling problems in a slotted system in which agents arrive with service requests according to a Bernoulli process and have to leave within two slots after arrival, service costs are quadratic in service rates, and there are also waiting costs. We consider quadratic waiting costs. We frame the problems as average cost Markov decision processes. While the studied system is a linear system with quadratic costs, it has state dependent control. Moreover, it also possesses a non-standard cost function structure in the case of fixed waiting costs, rendering the optimization problem complex. We characterize optimal policy. We provide an explicit expression showing that the optimal policy is linear in the system state. We also consider systems in which the agents make scheduling decisions for their respective service requests keeping their own cost in view. We consider quadratic waiting costs and frame these scheduling problems as stochastic games. We provide Nash equilibria of this game. To address the issue of unknown system parameters, we propose an algorithm to estimate them. We also bound the cost difference of the actual cost incurred and the cost incurred using e
This paper addresses the optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The paper first gives a fairly complete picture of the computational complexity of this optimization problem, its relation to optimiztion over the core itself, and its equivalence to other, minimal core relaxations that have been proposed earlier. We then address minimum cost spanning tree (MST) games as an example for a class of cost sharing games with non-empty core. While submodular cost functions yield efficient algorithms to maximize shareable costs, MST games have cost functions that are subadditive, but generally not submodular. Nevertheless, it is well known that cost shares in the core of MST games can be found efficiently. In contrast, we show that the maximization of shareable costs is NP-hard for MST games and derive a 2-approximation algorithm. Our work opens several directions for fu
Context: In-app advertising is the primary source of revenue for many mobile apps. The cost of advertising (ad cost) is non-negligible for app developers to ensure a good user experience and continuous profits. Previous studies mainly focus on addressing the hidden performance costs generated by ads, including consumption of memory, CPU, data traffic, and battery. However, there is no research onanalyzing users' perceptions of ads' performance costs to our knowledge. Objective: To fill this gap and better understand the effects of performance costs of in-app ads on user experience, we conduct a study on analyzing user concerns about ads' performance costs. Method: First, we propose RankMiner, an approach to quantify user concerns about specific appissues, including performance costs. Then, based on the usage traces of 20 subject apps, we measure the performance costs of ads. Finally, we conduct correlation analysis on the performance costs and quantified user concerns to explore whether users complain more for higher performance costs. Results: Our findings include the following: (1) RankMiner can quantify users' concerns better than baselines by an improvement of 214% and 2.5% in
The multi-scale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor network states motivated by the real-space renormalization group. It is used to simulate strongly correlated quantum many-body systems. For prominent MERA structures in one and two spatial dimensions and different optimization strategies, we determine the optimal scaling of contraction costs as well as corresponding contraction sequences and algorithmic phase diagrams. This is motivated by recent efforts to employ MERA in hybrid quantum-classical algorithms, where the MERA tensors are Trotterized, i.e., chosen as circuits of quantum gates, and observables as well as energy gradients are evaluated by sampling causal-cone states. We investigate whether tensor Trotterization and/or variational Monte Carlo (VMC) sampling can lead to quantum-inspired classical MERA algorithms that perform better than the traditional optimization of full MERA based on the exact evaluation of energy gradients. Algorithmic phase diagrams indicate the best MERA method depending on the scaling of the energy accuracy and the optimal number of Trotter steps with the bond dimension. The results suggest substantial gains
Along with the increasing frequency and severity of cyber incidents, understanding their economic implications is paramount. In this context, listed firms' reactions to cyber incidents are compelling to study since they (i) are a good proxy to estimate the costs borne by other organizations, (ii) have a critical position in the economy, and (iii) have their financial information publicly available. We extract listed firms' cyber incident dates and characteristics from newswire headlines. We use an event study over 2012--2022, using a three-day window around events and standard benchmarks. We find that the magnitude of abnormal returns around cyber incidents is on par with previous studies using newswire or alternative data to identify cyber incidents. Conversely, as we adjust the standard errors accounting for event-induced variance and residual cross-correlation, we find that the previously claimed significance of abnormal returns vanishes. Given these results, we run a horse race of specifications, in which we test for the marginal effects of type of cyber incidents, target firm sector, periods, and their interactions. Data breaches are the most detrimental incident type with an
This paper studies how gifts - monetary or in-kind payments - from drug firms to physicians in the US affect prescriptions and drug costs. We estimate heterogeneous treatment effects by combining physician-level data on antidiabetic prescriptions and payments with causal inference and machine learning methods. We find that payments cause physicians to prescribe more brand drugs, resulting in a cost increase of $30 per dollar received. Responses differ widely across physicians, and are primarily explained by variation in patients' out-of-pocket costs. A gift ban is estimated to decrease drug costs by 3-4%. Taken together, these novel findings reveal how payments shape prescription choices and drive up costs.
The problem of obtaining market-clearing prices for markets with non-convexities has been widely studied in the literature. This is particularly the case in electricity markets, where worldwide deregulation leads to markets in which non-convexities arise from the decisions of market operators regarding which generators are committed to provide electricity power. Here, we extend seminal results in this area to address the problem of obtaining market-clearing prices for markets in which beyond non-convexities, it is relevant to account for convex quadratic market costs. In a general market, such costs arise from quadratic commodity costs or transactions costs. In an electricity market, such quadratic costs arise when ramping costs need to be considered due to the presence of renewable energy sources, which continue to increase their participation in electricity markets. To illustrate our results, we compute and analyze the clearing prices of a classical market problem with the addition of ramping costs.
We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.
We consider the problem of Cost-Aware Learning, where sampling different components of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. We propose Cost-Aware SGD, which uses a distribution based on gradient norms and costs to sample components. We provide a thorough analysis of this algorithm, including cost-improvement bounds over baselines, a characterization of distribution proxy sub-optimality, and a lower bound. We apply our theoretical insights to reinforcement learning with language models, where the computational cost of sequence-level policy gradients varies with length. We find that the advantage magnitude serves as a high-fidelity proxy for gradient norms, and use this to introduce Cost-Aware GRPO. Empirical results on 1.5B, 4B, and 8B LLMs demonstrate that this algorithm significantly reduces the tokens used in policy optimization while matching or exceeding baseline accuracy.