We consider a multi-armed bandit problem specified by a set of one-dimensional family exponential distributions endowed with a unimodal structure. We introduce IMED-UB, an algorithm that optimally exploits the unimodal-structure, by adapting to this setting the Indexed Minimum Empirical Divergence (IMED) algorithm introduced by Honda and Takemura [2015]. Owing to our proof technique, we are able to provide a concise finite-time analysis of the IMED-UBalgorithm. Numerical experiments show that IMED-UBcompetes with the state-of-the-art algorithms.

We organize our supplementary document as follows: 1. Results on additional dataset 2. Results for limited data settings on YFCC26k and GWS15k datasets 3. Additional Ablations (a) Gallery Size (b) Queue Length (c) ση for Batch GPS noise (d) ση for Queue GPS noise (e) σ for Random Fourier Features (f) Number of hierarchies (M) 4. Different selection choices for GPSGallery Construction (a) Evenly Spaced GPSCoordinates (b) Test Set GPSCoordinates 5. Analysis of Runtime and Memory Footprint 6. Motivations for using Pretrained CLIP as Image encoder Backbone 7. Qualitative Demonstration (a) Hierarchical learning in our location encoder L () (b) GeoCLIP with Image Query (c) Distribution of correct predictions of GeoCLIP on different datasets (d) GeoCLIP with Text Query 8. Discussion on Ethical Issues and Possible Mitigation In section 4.1 of the main paper, we demonstrated the performance of our GeoCLIP method on Im2GPS3k [2] and GWS15k [1] datasets and compared them with the state-of-the-art methods. Here, we perform experiments on another dataset YFCC26k [6]. The results are provided in Table 1. This result highlights that GeoCLIP performs well across datasets, being useful across different data distributions. GeoCLIP achieves decent performance across datasets even when the training data is significantly reduced. 2 We show the efficacy of GeoCLIP on limited training samples of Im2GPS3k in section 4.2 of the main paper. Now, we further investigate the performance of GeoCLIP for limited data settings on other datasets (YFCC26k and GWS15k).

In this document, we provide additional details and results to the main paper. The document is structured as follows: A.1 Loss Analysis - Analysis of the unimodal and multimodal latent regularization loss across different distributions and an ablation study on the proposed loss function. A.2 Image Generation - In this section, we compare VQVAE model with our method, provide detailed descriptions of the dataset, network architecture, and implementation details of the image generation experiments in the main paper. A.3 Modelling Discrete Structures - In this section, we describe the experimental and implementation details of the discrete data structure experiments in the main paper. A.5 Additional Qualitative Analysis - More examples of the randomly generated samples of MNIST, FASHIONMNIST, SVHN and CELEBA images.