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“Lorem Ipsum”, Branwen 2020

Lorem: “Lorem Ipsum”⁠, Gwern Branwen (2020-09-27; ⁠, ⁠, ⁠, ; similar):

Systems stress-test page for Gwern.net functionality, exercising Markdown/​HTML/​CSS/​JS features at scale to check that they render correctly in mobile/​desktop.

Abstract of article summarizing the page. For design philosophy, see About⁠. This is a test page which exercises all standard functionality and features of Gwern.net, from standard Pandoc Markdown like blockquotes/​headers/​tables/​images, to custom features like sidenotes, margin notes, left/​right-floated and width-full images, columns, epigraphs, admonitions, small/​wide tables, smallcaps, collapse sections, link annotations, link icons.

User-visible bugs which may appear on this page: zooms into small rather than large original image (mobile).

“Sidenotes In Web Design”, Branwen 2020

Sidenotes: “Sidenotes In Web Design”⁠, Gwern Branwen (2020-08-06; ⁠, ⁠, ⁠, ; backlinks; similar):

In typography/​design, ‘sidenotes’ place footnotes/​endnotes in the margins for easier reading. I discuss design choices, HTML implementations and their pros/​cons.

Sidenotes/​margin notes are a typographic convention which improves on footnotes & endnotes by instead putting the notes in the page margin to let the reader instantly read them without needing to refer back and forth to the end of the document (endnotes) or successive pages (footnotes spilling over).

They are particularly useful for web pages, where ‘footnotes’ are de facto endnotes, and clicking back and forth to endnotes is a pain for readers. (Footnote variants, like “floating footnotes” which pop up on mouse hover, reduce the reader’s effort but don’t eliminate it.)

However, they are not commonly used, perhaps because web browsers until relatively recently made it hard to implement sidenotes easily & reliably. Tufte-CSS has popularized the idea and since then, there has been a proliferation of slightly variant approaches. I review some of the available implementations.

For general users, I recommend Tufte-CSS: it is fast & simple (using only compile-time generation of sidenotes, rendered by static HTML/​CSS), popular, and easy to integrate into most website workflows. For heavy footnote users or users who want a drop-in, runtime Javascript-based solutions like sidenotes.js may be more useful.

“The Kelly Coin-Flipping Game: Exact Solutions”, Branwen et al 2017

Coin-flip: “The Kelly Coin-Flipping Game: Exact Solutions”⁠, Gwern Branwen, Arthur B., nshepperd, FeepingCreature, Gurkenglas (2017-01-19; ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ; backlinks; similar):

Decision-theoretic analysis of how to optimally play Haghani & Dewey 2016’s 300-round double-or-nothing coin-flipping game with an edge and ceiling better than using the Kelly Criterion. Computing and following an exact decision tree increases earnings by $6.6 over a modified KC.

Haghani & Dewey 2016 experiment with a double-or-nothing coin-flipping game where the player starts with $30.4[^\$25.0^~2016~]{.supsub} and has an edge of 60%, and can play 300 times, choosing how much to bet each time, winning up to a maximum ceiling of $303.8[^\$250.0^~2016~]{.supsub}. Most of their subjects fail to play well, earning an average $110.6[^\$91.0^~2016~]{.supsub}, compared to Haghani & Dewey 2016’s heuristic benchmark of ~$291.6[^\$240.0^~2016~]{.supsub} in winnings achievable using a modified Kelly Criterion as their strategy. The KC, however, is not optimal for this problem as it ignores the ceiling and limited number of plays.

We solve the problem of the value of optimal play exactly by using decision trees & dynamic programming for calculating the value function, with implementations in R, Haskell⁠, and C. We also provide a closed-form exact value formula in R & Python, several approximations using Monte Carlo/​random forests⁠/​neural networks, visualizations of the value function, and a Python implementation of the game for the OpenAI Gym collection. We find that optimal play yields $246.61 on average (rather than ~$240), and so the human players actually earned only 36.8% of what was possible, losing $155.6 in potential profit. Comparing decision trees and the Kelly criterion for various horizons (bets left), the relative advantage of the decision tree strategy depends on the horizon: it is highest when the player can make few bets (at b = 23, with a difference of ~$36), and decreases with number of bets as more strategies hit the ceiling.

In the Kelly game, the maximum winnings, number of rounds, and edge are fixed; we describe a more difficult generalized version in which the 3 parameters are drawn from Pareto, normal, and beta distributions and are unknown to the player (who can use Bayesian inference to try to estimate them during play). Upper and lower bounds are estimated on the value of this game. In the variant of this game where subjects are not told the exact edge of 60%, a Bayesian decision tree approach shows that performance can closely approach that of the decision tree, with a penalty for 1 plausible prior of only $1. Two deep reinforcement learning agents, DQN & DDPG⁠, are implemented but DQN fails to learn and DDPG doesn’t show acceptable performance, indicating better deep RL methods may be required to solve the generalized Kelly game.

“A/B Testing Long-form Readability on Gwern.net”, Branwen 2012

AB-testing: “A/B testing long-form readability on Gwern.net”⁠, Gwern Branwen (2012-06-16; ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, ; backlinks; similar):

A log of experiments done on the site design, intended to render pages more readable, focusing on the challenge of testing a static site, page width, fonts, plugins, and effects of advertising.

To gain some statistical & web development experience and to improve my readers’ experiences, I have been running a series of CSS A/​B tests since June 2012. As expected, most do not show any meaningful difference.

Miscellaneous