MNL-Bandit with Knapsacks: a near-optimal algorithm
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911763568525312 |
|---|---|
| author | Aznag, Abdellah Goyal, Vineet Perivier, Noemie |
| author_facet | Aznag, Abdellah Goyal, Vineet Perivier, Noemie |
| contents | We consider a dynamic assortment selection problem where a seller has a fixed inventory of $N$ substitutable products and faces an unknown demand that arrives sequentially over $T$ periods. In each period, the seller needs to decide on the assortment of products (satisfying certain constraints) to offer to the customers. The customer's response follows an unknown multinomial logit model (MNL) with parameter $\boldsymbol{v}$. If customer selects product $i \in [N]$, the seller receives revenue $r_i$. The goal of the seller is to maximize the total expected revenue from the $T$ customers given the fixed initial inventory of $N$ products. We present MNLwK-UCB, a UCB-based algorithm and characterize its regret under different regimes of inventory size. We show that when the inventory size grows quasi-linearly in time, MNLwK-UCB achieves a $\tilde{O}(N + \sqrt{NT})$ regret bound. We also show that for a smaller inventory (with growth $\sim T^α$, $α< 1$), MNLwK-UCB achieves a $\tilde{O}(N(1 + T^{\frac{1 - α}{2}}) + \sqrt{NT})$. In particular, over a long time horizon $T$, the rate $\tilde{O}(\sqrt{NT})$ is always achieved regardless of the constraints and the size of the inventory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_01135 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | MNL-Bandit with Knapsacks: a near-optimal algorithm Aznag, Abdellah Goyal, Vineet Perivier, Noemie Machine Learning Data Structures and Algorithms We consider a dynamic assortment selection problem where a seller has a fixed inventory of $N$ substitutable products and faces an unknown demand that arrives sequentially over $T$ periods. In each period, the seller needs to decide on the assortment of products (satisfying certain constraints) to offer to the customers. The customer's response follows an unknown multinomial logit model (MNL) with parameter $\boldsymbol{v}$. If customer selects product $i \in [N]$, the seller receives revenue $r_i$. The goal of the seller is to maximize the total expected revenue from the $T$ customers given the fixed initial inventory of $N$ products. We present MNLwK-UCB, a UCB-based algorithm and characterize its regret under different regimes of inventory size. We show that when the inventory size grows quasi-linearly in time, MNLwK-UCB achieves a $\tilde{O}(N + \sqrt{NT})$ regret bound. We also show that for a smaller inventory (with growth $\sim T^α$, $α< 1$), MNLwK-UCB achieves a $\tilde{O}(N(1 + T^{\frac{1 - α}{2}}) + \sqrt{NT})$. In particular, over a long time horizon $T$, the rate $\tilde{O}(\sqrt{NT})$ is always achieved regardless of the constraints and the size of the inventory. |
| title | MNL-Bandit with Knapsacks: a near-optimal algorithm |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2106.01135 |