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In retail warehouses, returned products are typically placed in an intermediate storage until a decision regarding further shipment to stores is made. The longer products are held in storage, the higher the inefficiency and costs of the returns management process, since enough storage area has to be provided and maintained while the products are not placed for sale. To reduce the average product storage time, we consider an alternative solution where reallocation decisions for products can be made instantly upon their arrival in the warehouse allowing only a limited number of products to still be stored simultaneously. We transfer the problem to an online multiple knapsack problem and propose a novel reinforcement learning approach to pack the items (products) into the knapsacks (stores) such that the overall value (expected revenue) is maximized. Empirical evaluations on simulated data demonstrate that, compared to the usual offline decision procedure, our approach comes with a performance gap of only 3% while significantly reducing the average storage time of a product by 96%.

Efforts to reduce platelet wastage in hospital blood banks have focused on ordering policies, but the predominant practice of issuing the oldest unit first may not be optimal when some units are returned unused. We propose a novel, machine learning (ML)-guided issuing policy to increase the likelihood of returned units being reissued before expiration. Our ML model trained to predict returns on 17,297 requests for platelets gave AUROC 0.74 on 9,353 held-out requests. Prior to ML model development we built a simulation of the blood bank operation that incorporated returns to understand the scale of benefits of such a model. Using our trained model in the simulation gave an estimated reduction in wastage of 14%. Our partner hospital is considering adopting our approach, which would be particularly beneficial for hospitals with higher return rates and where units have a shorter remaining useful life on arrival.

The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology $\check H^1(Ω)$ gives upper and lower bounds for the size of the return module. For all sufficiently large patches, the rank of the return module is at most the same as the rank of the cohomology. For a generic choice of tile shapes and an arbitrary reference patch, the rank of the return module is at least the rank of $\check H^1(Ω)$. Therefore, for generic tile shapes and sufficiently large patches, the rank of the return module is equal to the rank of $\check H^1(Ω)$.

Traditional approaches in offline reinforcement learning aim to learn the optimal policy that maximizes the cumulative reward, also known as return. It is increasingly important to adjust the performance of AI agents to meet human requirements, for example, in applications like video games and education tools. Decision Transformer (DT) optimizes a policy that generates actions conditioned on the target return through supervised learning and includes a mechanism to control the agent's performance using the target return. However, the action generation is hardly influenced by the target return because DT's self-attention allocates scarce attention scores to the return tokens. In this paper, we propose Return-Aligned Decision Transformer (RADT), designed to more effectively align the actual return with the target return. RADT leverages features extracted by paying attention solely to the return, enabling action generation to consistently depend on the target return. Extensive experiments show that RADT significantly reduces the discrepancies between the actual return and the target return compared to DT-based methods. Our code is available at https://github.com/CyberAgentAILab/radt

We examine how large language models (LLMs) interpret historical stock returns and compare their forecasts with estimates from a crowd-sourced platform for ranking stocks. While stock returns exhibit short-term reversals, LLM forecasts over-extrapolate, placing excessive weight on recent performance similar to humans. LLM forecasts appear optimistic relative to historical and future realized returns. When prompted for 80% confidence interval predictions, LLM responses are better calibrated than survey evidence but are pessimistic about outliers, leading to skewed forecast distributions. The findings suggest LLMs manifest common behavioral biases when forecasting expected returns but are better at gauging risks than humans.

Resetting, in which a system is regularly returned to a given state after a fixed or random duration, has become a useful strategy to optimize the search performance of a system. While earlier theoretical frameworks focused on instantaneous resetting, wherein the system is directly teleported to a given state, there is a growing interest in physical resetting mechanisms that involve a finite return time. However employing such a mechanism involves cost and the effect of this cost on the search time remains largely unexplored. Yet answering this is important in order to design cost-efficient resetting strategies. Motivated from this, we present a thermodynamic analysis of a diffusing particle whose position is intermittently reset to a specific site by employing a stochastic return protocol with external confining trap. We show for a family of potentials $U_R(x) \sim |x|^{m}$ with $m>0$, it is possible to find optimal potential shape that minimises the expected first-passage time for a given value of the thermodynamic cost, i.e. mean work. By varying this value, we then obtain the Pareto optimal front, and demonstrate a trade-off relation between the first-passage time and the wo

It is a challenge to estimate fund performance by compounded returns. Arguably, it is incorrect to use yearly returns directly for compounding, with reported annualized return of above 60% for Medallion for the 31 years up to 2018. We propose an estimation based on fund sizes and trading profits and obtain a compounded return of 31.8% before fees. Alternatively, we suggest using the manager's wealth as a proxy and arriving at a compounded growth rate of 25.6% for Simons for the 33 years up to 2020. We conclude that the annualized compounded return of Medallion before fees is probably under 35%. Our findings have implications for correctly estimating fund performance.

Search prominence may have a detrimental impact on a firm's profits in the presence of costly product returns. We analyze the impact of search prominence on firm profitability in a duopoly search model, considering the presence of costly product returns. Consumer match values are assumed to be independently and identically distributed across the two products. Our results show that the non-prominent firm benefits from facing consumers with relatively low match values for the prominent firm's products, thus avoiding costly returns. When return costs are sufficiently high, the prominent firm may earn lower profits than its non-prominent competitor. This outcome holds under both price exogeneity and price competition. Furthermore, the profitability advantage of prominence diminishes as return costs increase. Platforms that maximize ad revenue should consider retaining positive return cost for consumers rather than fully passing it on to firms. For e-commerce platforms, it is crucial to align product return policies with broader management objectives to optimize firm profitability.

This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the definition of market-based average return of trades during the averaging period. Then we derive the dependence of market-based volatility and higher statistical moments of returns on statistical moments, volatilities, and correlations of the current and past trade values. We derive the approximations of the characteristic function and the probability of returns by a finite number q of market-based statistical moments. To forecast market-based average and volatility of returns at horizon T, one should predict the first two statistical moments and correlation of current and past trade values at the same horizon. We discuss the economic reasons that limit the number of predicted statistical moments of returns by the first two. That limits the accuracy of the forecasts of probability of returns by the accuracy of the Gaussian approximations. To improve the reliability of large macroeconomic and market models like BlackRock's Aladdin, JP Morgan, and the

Informally, a risk measure is said to be elicitable if there exists a suitable scoring function such that minimizing its expected value recovers the risk measure. In this paper, we analyze the elicitability properties of the class of return risk measures (i.e., normalized, monotone and positively homogeneous risk measures). First, we provide dual representation results for convex and geometrically convex return risk measures. Next, we establish new axiomatic characterizations of Orlicz premia (i.e., Luxemburg norms). More specifically, we prove, under different sets of conditions, that Orlicz premia naturally arise as the only elicitable return risk measures. Finally, we provide a general family of strictly consistent scoring functions for Orlicz premia, a myriad of specific examples and a mixture representation suitable for constructing Murphy diagrams.

We propose a Holistic Return on Ethics (HROE) framework for understanding the return on organizational investments in artificial intelligence (AI) ethics efforts. This framework is useful for organizations that wish to quantify the return for their investment decisions. The framework identifies the direct economic returns of such investments, the indirect paths to return through intangibles associated with organizational reputation, and real options associated with capabilities. The holistic framework ultimately provides organizations with the competency to employ and justify AI ethics investments.

We describe how the market-based average and volatility of the "actual" return, which the investors gain within their market sales, depend on the statistical moments, volatilities, and correlations of the current and past market trade values. We describe three successive approximations. First, we derive the dependence of the market-based average and volatility of a single sale return on market trade statistical moments determined by multiple purchases in the past. Then, we describe the dependence of average and volatility of return that a single investor gains during the "trading day." Finally, we derive the market-based average and volatility of return of different investors during the "trading day" as a function of volatilities and correlations of market trade values. That highlights the distribution of the "actual" return of market trade and can serve as a benchmark for "purchasing" investors.

Decentralized Finance (DeFi) is a nascent set of financial services, using tokens, smart contracts, and blockchain technology as financial instruments. We investigate four possible drivers of DeFi returns: exposure to cryptocurrency market, the network effect, the investor's attention, and the valuation ratio. As DeFi tokens are distinct from classical cryptocurrencies, we design a new dedicated market index, denoted DeFiX. First, we show that DeFi tokens returns are driven by the investor's attention on technical terms such as "decentralized finance" or "DeFi", and are exposed to their own network variables and cryptocurrency market. We construct a valuation ratio for the DeFi market by dividing the Total Value Locked (TVL) by the Market Capitalization (MC). Our findings do not support the TVL/MC predictive power assumption. Overall, our empirical study shows that the impact of the cryptocurrency market on DeFi returns is stronger than any other considered driver and provides superior explanatory power.

We study the effect of returning radiation on the shape of the X-ray reflection spectrum in the case of thin accretion disks. We show that the returning radiation mainly influences the observed reflection spectrum for a large black hole spin (a > 0.9) and a compact primary source of radiation close to the black hole at height h < 5 $r_\mathrm{g}$, and that it dominates the reflected flux for extreme values of spin and compactness. The main effect of the returning radiation is to increase the irradiating flux on to the outer parts of the accretion disk, leading to stronger reflection and a flatter overall emissivity profile. By analyzing simulated observations we show that neglecting returning radiation in existing studies of reflection dominated sources has likely resulted in overestimating the height of the corona above the black hole. An updated version of the publicly available relxill suite of relativistic reflection models which includes returning radiation is also presented.

This article considers a stable vector autoregressive (VAR) model and investigates return predictability in a Bayesian context. The VAR system comprises asset returns and the dividend-price ratio as proposed in Cochrane (2008), and allows pinning down the question of return predictability to the value of one particular model parameter. We develop a new shrinkage type prior for this parameter and compare our Bayesian approach to ordinary least squares estimation and to the reduced-bias estimator proposed in Amihud and Hurvich (2004). A simulation study shows that the Bayesian approach dominates the reduced-bias estimator in terms of observed size (false positive) and power (false negative). We apply our methodology to annual CRSP value-weighted returns running, respectively, from 1926 to 2004 and from 1953 to 2021. For the first sample, the Bayesian approach supports the hypothesis of no return predictability, while for the second data set weak evidence for predictability is observed.

With the rapid growth in fashion e-commerce and customer-friendly product return policies, the cost to handle returned products has become a significant challenge. E-tailers incur huge losses in terms of reverse logistics costs, liquidation cost due to damaged returns or fraudulent behavior. Accurate prediction of product returns prior to order placement can be critical for companies. It can facilitate e-tailers to take preemptive measures even before the order is placed, hence reducing overall returns. Furthermore, finding return probability for millions of customers at the cart page in real-time can be difficult. To address this problem we propose a novel approach based on Deep Neural Network. Users' taste & products' latent hidden features were captured using product embeddings based on Bayesian Personalized Ranking (BPR). Another set of embeddings was used which captured users' body shape and size by using skip-gram based model. The deep neural network incorporates these embeddings along with the engineered features to predict return probability. Using this return probability, several live experiments were conducted on one of the major fashion e-commerce platform in order t

The mass returned to the ambient medium by aging stellar populations over cosmological times sums up to a significant fraction (20% - 30% or more) of their initial mass. This continuous mass injection plays a fundamental role in phenomena such as galaxy formation and evolution, fueling of supermassive black holes in galaxies and the consequent (negative and positive) feedback phenomena, and the origin of multiple stellar populations in globular clusters. In numerical simulations the calculation of the mass return can be time consuming, since it requires at each time step the evaluation of a convolution integral over the whole star formation history, so the computational time increases quadratically with the number of time-steps. The situation can be especially critical in hydrodynamical simulations, where different grid points are characterized by different star formation histories, and the gas cooling and heating times are shorter by orders of magnitude than the characteristic stellar lifetimes. In this paper we present a fast and accurate method to compute the mass return from stellar populations undergoing arbitrarily complicated star formation histories. At each time-step the m