Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Perishability of Data: Dynamic Pricing under Varying-Coefficient Models
Authors: Adel Javanmard
JMLR 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We numerically study the performance of our PSGD pricing policy on synthetic data. In our experiments, we set W = 5 and set θ1 = (W/2)(Z/ Z ), with Z N(0, Id) a multivariate normal variable. We then generate a sequence of parameters θt as follows: θt+1 = θt + rt , where rt = t b( Z/ Z ), with Z N(0, Id). Note that δt = θt+1 θt = rt = t b. Next, at each time t, product covariates xt are independently sampled from a Gaussian distribution N(0, Id) and normalized so that xt = 1. Further, the market shocks are generated as zt N(0, σ2), with σ = 1. We run the PSGD pricing policy for stochastic features model. Results. Figure 1 compares the cumulative regret (averaged over 80 trials) of the PSGD policy, for b = 0.5, 1, 2, on the aforementioned synthetic data for T = 50, 000 steps. The shaded region around each curve correspond to the 95% confidence interval across the 80 trials. As expected, increase in b results in larger temporal variations and larger regret. To better understand the behavior of regret for different values of b, we plotted the regret bounds in various scales in Figure 2. For b = 0.5, we have Regret(T) T 2/3, and for b = 1, 2, we have Regret log(T). Comparing with Theorem 7, we see that the empirical regret in case of b = 0.5, 1, is smaller than the upper bound given by Equation (28), order-wise. However, it is worth noting that bound given in Theorem 7 applies to any adversarial choice of temporal variations rt, while in our experiments we generated these terms independently at random. |
| Researcher Affiliation | Academia | Adel Javanmard EMAIL Department of Data Sciences and Operations Marshall School of Business University of Southern California Los Angeles, CA 90089 , USA |
| Pseudocode | Yes | PSGD (Projected stochastic gradient descent) pricing policy Input: (at time 0) function g, set Θ, Input: (arrives over time) covariate vectors {xt}t N Output: prices {pt}t N 1: p1 0 and initialize bθ1 Θ 2: for t = 1, 2, 3, . . . do 3: Set bθt+1 according to the following rule: bθt+1 = ΠΘ(bθt ηt ℓt(bθt)) (11) ℓt(θ) = I(yt = 1) log(1 F(pt xt, θ )) I(yt = 1) log(F(pt xt, θ )) (12) 4: Set price pt+1 as pt+1 g( xt+1, bθt+1 ) (13) |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating the release of open-source code for the methodology described. |
| Open Datasets | No | We numerically study the performance of our PSGD pricing policy on synthetic data. |
| Dataset Splits | No | We numerically study the performance of our PSGD pricing policy on synthetic data. ... at each time t, product covariates xt are independently sampled from a Gaussian distribution N(0, Id) and normalized so that xt = 1. Further, the market shocks are generated as zt N(0, σ2), with σ = 1. This describes data generation, not splitting. |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers. |
| Experiment Setup | Yes | In our experiments, we set W = 5 and set θ1 = (W/2)(Z/ Z ), with Z N(0, Id) a multivariate normal variable. We then generate a sequence of parameters θt as follows: θt+1 = θt + rt , where rt = t b( Z/ Z ), with Z N(0, Id). Note that δt = θt+1 θt = rt = t b. Next, at each time t, product covariates xt are independently sampled from a Gaussian distribution N(0, Id) and normalized so that xt = 1. Further, the market shocks are generated as zt N(0, σ2), with σ = 1. We run the PSGD pricing policy for stochastic features model. ... for T = 50, 000 steps. |