This project implements GAdaOFUL, a robust online bandit learning algorithm designed to handle nonlinear rewards and corrupted feedback. The algorithm is tested against state-of-the-art baselines in various environments, demonstrating superior performance in terms of regret minimization and robustness.

• 🛡️ Robustness: Handles heavy-tailed noise (t-distributed) and adversarial corruption.
• 📈 Nonlinear Rewards: Supports exponential reward mappings and general monotonic functions.
• 🔍 Dynamic Environments: Works with time-varying decision sets.
• 📊 Benchmarking: Includes implementations of 5 baseline algorithms (Greedy, OFUL, CW-OFUL, AdaOFUL).

We perform numerical experiments in a 10-dimensional space $d = 10$, using a unit sphere for the target vector $\theta^*$, and conduct trials to compare different algorithms under various conditions. The setup includes:

• Decision Set: At each step, a decision set $D_t$ of 20 random unit vectors is generated.

• Noise Distribution: Noise is drawn from a heavy-tailed $t$-distribution with 3 degrees of freedom $t_3$.

• Nonlinear Reward Function: Rewards are mapped using the exponential function $y = \exp(x)$, where $x \in [-1,1]$.

• Corruption: During the first $n = 50$ steps, we simulate reward corruption using the flipping technique, where the reward is intentionally flipped to mislead the bandit into making opposite decisions.

• Modify parameters in gada1.ipynb as needed:

This code is based on the implementation of CW-OFUL. Thanks for their excellent works!