This paper proposes a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a population of $m$ users, arrives. The decision-maker observes the user and selects an item from a catalogue of $n$ items. Importantly, an item cannot be recommended twice to the same user. The probabilities that a user likes each item are unknown, and the performance of the recommendation algorithm is captured through its regret, considering as a reference an Oracle algorithm aware of these probabilities. We investigate various structural assumptions on these probabilities: we derive for each of them regret lower bounds, and devise algorithms achieving these limits. Interestingly, our analysis reveals the relative weights of the different components of regret: the component due to the constraint of not presenting the same item twice to the same user, that due to learning the chances users like items, and finally that arising when learning the underlying structure.

ID-based embeddings are widely used in web-scale online recommendation systems. However, their susceptibility to overfitting, particularly due to the long-tail nature of data distributions, often limits training to a single epoch, a phenomenon known as the "one-epoch problem." This challenge has driven research efforts to optimize performance within the first epoch by enhancing convergence speed or feature sparsity. In this study, we introduce a novel two-stage training strategy that incorporates a pre-training phase using a minimal model with contrastive loss, enabling broader data coverage for the embedding system. Our offline experiments demonstrate that multi-epoch training during the pre-training phase does not lead to overfitting, and the resulting embeddings improve online generalization when fine-tuned for more complex downstream recommendation tasks. We deployed the proposed system in live traffic at Pinterest, achieving significant site-wide engagement gains.

Weaknesses: My main observation is that the paper does not clearly compares the regret bounds it obtains with existing literature. I find the presentation of the regret bounds to be fairly non-standard and hard to interpret. These are some of my concerns. It seems to me that R_sp(T) is just a standard K-armed bandit lower bound which can be applied here by the reduction to the case where the cluster identity of each item is known, but {p_1, ..., p_K} needs to be learned. On the other hand, R_{ic} just seems to be something coming from running out of items to recommend from the top cluster and a bound on the size of such a cluster because of the sampling from {\alpha}'s initially.

The reviewers warmed up to this paper during the discussion. Its scores increased from (5, 5, 6, 7) to (6, 6, 6, 7). Although we agreed that there are shortcomings, there are also new results. So the paper is worth accepting. My additional comments are below: 1) The title is indeed confusing.

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the "online" setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation systems, cast item recommendation under the model as a learning problem, and analyze the performance of a cosine-similarity collaborative filtering method. In our model, each of n users either likes or dislikes each of m items. We assume there to be k types of users, and all the users of a given type share a common string of probabilities determining the chance of liking each item. At each time step, we recommend an item to each user, where a key distinction from related bandit literature is that once a user consumes an item (e.g., watches a movie), then that item cannot be recommended to the same user again. The goal is to maximize the number of likable items recommended to users over time. Our main result establishes that after nearly log(km) initial learning time steps, a simple collaborative filtering algorithm achieves essentially optimal performance without knowing k. The algorithm has an exploitation step that uses cosine similarity and two types of exploration steps, one to explore the space of items (standard in the literature) and the other to explore similarity between users (novel to this work).

This paper proposes a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a population of m users, arrives. The decision-maker observes the user and selects an item from a catalogue of n items. Importantly, an item cannot be recommended twice to the same user. The probabilities that a user likes each item are unknown, and the performance of the recommendation algorithm is captured through its regret, considering as a reference an Oracle algorithm aware of these probabilities.

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the "online" setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation systems, cast item recommendation under the model as a learning problem, and analyze the performance of a cosine-similarity collaborative filtering method. In our model, each of n users either likes or dislikes each of m items. We assume there to be k types of users, and all the users of a given type share a common string of probabilities determining the chance of liking each item. At each time step, we recommend an item to each user, where a key distinction from related bandit literature is that once a user consumes an item (e.g., watches a movie), then that item cannot be recommended to the same user again. The goal is to maximize the number of likable items recommended to users over time. Our main result establishes that after nearly log(km) initial learning time steps, a simple collaborative filtering algorithm achieves essentially optimal performance without knowing k. The algorithm has an exploitation step that uses cosine similarity and two types of exploration steps, one to explore the space of items (standard in the literature) and the other to explore similarity between users (novel to this work).

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the ``online'' setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation systems, cast item recommendation under the model as a learning problem, and analyze the performance of a cosine-similarity collaborative filtering method. In our model, each of $n$ users either likes or dislikes each of $m$ items. We assume there to be $k$ types of users, and all the users of a given type share a common string of probabilities determining the chance of liking each item. At each time step, we recommend an item to each user, where a key distinction from related bandit literature is that once a user consumes an item (e.g., watches a movie), then that item cannot be recommended to the same user again. The goal is to maximize the number of likable items recommended to users over time. Our main result establishes that after nearly $\log(km)$ initial learning time steps, a simple collaborative filtering algorithm achieves essentially optimal performance without knowing $k$. The algorithm has an exploitation step that uses cosine similarity and two types of exploration steps, one to explore the space of items (standard in the literature) and the other to explore similarity between users (novel to this work).

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the "online" setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation systems, cast item recommendation under the model as a learning problem, and analyze the performance of a cosine-similarity collaborative filtering method. In our model, each of $n$ users either likes or dislikes each of $m$ items. We assume there to be $k$ types of users, and all the users of a given type share a common string of probabilities determining the chance of liking each item. At each time step, we recommend an item to each user, where a key distinction from related bandit literature is that once a user consumes an item (e.g., watches a movie), then that item cannot be recommended to the same user again. The goal is to maximize the number of likable items recommended to users over time. Our main result establishes that after nearly $\log(km)$ initial learning time steps, a simple collaborative filtering algorithm achieves essentially optimal performance without knowing $k$. The algorithm has an exploitation step that uses cosine similarity and two types of exploration steps, one to explore the space of items (standard in the literature) and the other to explore similarity between users (novel to this work).