Memoryless Sequences for General Losses
Authors: Rafael Frongillo, Andrew Nobel
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we address the question of how changing the loss function changes the set of memoryless sequences, and in particular, the stochastic attributes they possess. For convex differentiable losses we establish that the statistic or property elicited by the loss determines the identity and stochastic attributes of the corresponding memoryless sequences. We generalize these results to convex non-differentiable losses, under additional assumptions, and to non-convex Bregman divergences. In particular, our results show that any Bregman divergence has the same set of memoryless sequences as squared loss. We apply our results to price calibration in prediction markets. |
| Researcher Affiliation | Academia | Rafael Frongillo EMAIL CU Boulder Andrew Nobel EMAIL UNC Chapel Hill |
| Pseudocode | Yes | Market maker initializes state x0 0 Rd for all traders t = 1, . . . , T do Trader t decides to purchase bundle rt Rd Market maker updates the state xt xt 1 + rt Trader pays the market maker C(xt) C(xt 1) end Outcome z Z is revealed and market maker pays rt, φ(z) to trader t = 1, . . . , T Algorithm 1: The cost-function-based market maker |
| Open Source Code | No | The paper does not contain any explicit statements about the release of source code for the methodology described, nor does it provide any links to a code repository. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical studies using specific datasets. Therefore, no information about open datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not conduct empirical studies using specific datasets. Therefore, no information about dataset splits is provided. |
| Hardware Specification | No | The paper focuses on theoretical contributions and does not describe any experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental implementation. Therefore, no specific software dependencies with version numbers are mentioned. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup, hyperparameters, or training configurations. |