Definition Consider a discrete-time Bandit Process with one arm (dropping arm index $i$ for convenience): Markov state transition, binary action, reward associated with positive action (aka ‘pull’) denoted as $r(x(t))$ at each time point $t = 1, \ldots$ The states $x(t)$ doesn’t change if the arm is idle. And the goal is to maximize the discounted reward criteria: $$ \text{Reward}:=\mathbb E[\sum_t \beta^t r(x(t))]. $$ ($x(\cdot)$ or $x$ is state) The Gittins Index $v(x)$ is calculated for each state $x$ as ...

In the standard discounted multi‑armed bandit (MAB) with binary “play/rest” decisions, Gittins’ index gives a provably optimal per‑arm priority rule. Section 3.2 of Q. Zhao (2021) For general bandit super process, index-based policy no longer works. Counterexample: Section 3.2 of Q. Zhao (2021) Actually, in many cases, the index is not even defined. But somehow if the problem is “indexable” satisfying the following condition, Index Policy still is optimal ...

Tired of df.head() giving you a mysterious “…”? When working with wide DataFrames, pandas hides columns by default—really? This simple line ensures every column stands proudly in your console: import pandas as pd pd.set_option('display.max_columns', None) # Show all columns Default slicing of data really drives people crazy. To solve this, one usually has to switch to VSCode or other graphic-based ipynb consoles for better visuals. But even in termainl, the full DataFrame view is just one setting away. ...

Schumann’s Kinderszenen (Op. 15) is not really meant for kids—it’s like a memory-scape written from adulthood, looking backward with tenderness, longing, and the complexity only hindsight can afford. The simplicity of the music is deceptive. It’s technically accessible “Leichte Stücke”—but emotionally layered. Happy children’s day :)

Duanwu, also known as the Dragon Boat Festival, is a traditional Chinese holiday celebrated on the 5th day of the 5th lunar month. It commemorates Qu Yuan, a patriotic poet who lived—and died—for his country over 2,000 years ago. But for me, Duanwu means something more personal. It marks the true beginning of summer—thick with heat, humidity, and a kind of restless energy. It’s a season that feels chaotic, slightly uncomfortable, yet oddly peaceful. Everything about this festival is part of my comfort zone. The traditions. The food—especially zongzi (sticky rice dumplings), my all-time favorite. The heat. It all brings me back to childhood, to a place I belong. ...

Here’s an interesting article about Spotify’s music recommendation algorithm: The surprising thing I learned from quitting Spotify Vox | Ada Estes | https://www.vox.com/even-better/404896/spotify-youtube-apple-music-amazon-playlists Spotify’s success key is the platform’s superior recommendation algorithm. What distinguishes Spotify is its 15-year archive of the user’s listening habits and an advanced algorithm that understands and reinforces personal tastes — something competitors like Apple Music failed to replicate (hmm?). Spotify’s strength lies in its hybrid use of content-based filtering (analyzing song attributes like genre, mood, and artist) and collaborative filtering (recommending music based on what similar users enjoy). With access to the listening patterns of 675 million users, Spotify can create surprisingly effective and serendipitous recommendations. ...

Believe it or not, ChatGPT dug this up for me among the ocean of economic literature! Recommender Systems as Mechanisms for Social Learning QJE 2017 | Yeon-Koo Che , Johannes Hörner. https://doi.org/10.1093/qje/qjx044 This article studies how a recommender system may incentivize users to learn about a product collaboratively. To improve the incentives for early exploration, the optimal design trades off fully transparent disclosure by selectively overrecommending the product (or “spamming”) to a fraction of users. Under the optimal scheme, the designer spams very little on a product immediately after its release but gradually increases its frequency; she stops it altogether when she becomes sufficiently pessimistic about the product. The recommender’s product research and intrinsic/naive users “seed” incentives for user exploration and determine the speed and trajectory of social learning. Potential applications for various Internet recommendation platforms and implications for review/ratings inflation are discussed. ...

There’s a thread in Reddit “If someone ask why did you watch Lolita. What will be your answer?” The famous poster — For research purposes, thank you! Ennio Morricone (1928–2020) was an Italian composer and conductor best known for his prolific work in film music. He scored over 400 films and television series. He received two Academy Awards, three Grammys and three Golden Globes. Works includes The Good, the Bad and the Ugly (1966), Once Upon a Time in the West (1968), and Cinema Paradiso (1988) and The Legend of 1900 (1998), and ...

I used to think Newton’s method was a bit old-school. Turns out I was the one playing catch-up. This is about Newton’s method and a clever way to make it work for constrained optimization. Consider optimizing an unconstrained function $f(\cdot)$ whose Hessian exists. Newton’s method works around its gradient function, finding a point $x^\star$ such that $\nabla f(x^\star) = 0$. In an iterative way, at each point $x^k$, it approximates the gradient function $\nabla f(\cdot)$ around $x^k$ using its second-order derivative information ...

Best known for his intimate, almost translucent interpretations of Debussy and Ravel, Gieseking’s style has long divided listeners. Some dismiss his playing as emotionally distant or overly plain (me). But others say it’s a refusal to overstate (almost me). Like, take his Debussy as an example—most pianist lean into impressionism drama. Eg., the master of which: Gieseking’s moonlight is like, wind whisper through water. He lets those notes hang like breath and his pedaling is nearly, invisible. There’s no excess ornament, no indulgence (to me), ...