Stochastic Online Learning with Probabilistic Graph Feedback

We consider a problem of stochastic online learning with general probabilistic graph feedback, where each directed edge in the feedback graph has probability $p_{ij}$. Two cases are covered. (a) The one-step case, where after playing arm $i$ the learner observes a sample reward feedback of arm $j$ with independent probability $p_{ij}$. (b) The cascade case where after playing arm $i$ the learner observes feedback of all arms $j$ in a probabilistic cascade starting from $i$ -- for each $(i,j)$ with probability $p_{ij}$, if arm $i$ is played or observed, then a reward sample of arm $j$ would be observed with independent probability $p_{ij}$. Previous works mainly focus on deterministic graphs which corresponds to one-step case with $p_{ij} \in \{0,1\}$, an adversarial sequence of graphs with certain topology guarantees, or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability

Sequential learning without feedback

In many security and healthcare systems a sequence of features/sensors/tests are used for detection and diagnosis. Each test outputs a prediction of the latent state, and carries with it inherent costs. Our objective is to {\it learn} strategies for selecting tests to optimize accuracy \& costs. Unfortunately it is often impossible to acquire in-situ ground truth annotations and we are left with the problem of unsupervised sensor selection (USS). We pose USS as a version of stochastic partial monitoring problem with an {\it unusual} reward structure (even noisy annotations are unavailable). Unsurprisingly no learner can achieve sublinear regret without further assumptions. To this end we propose the notion of weak-dominance. This is a condition on the joint probability distribution of test outputs and latent state and says that whenever a test is accurate on an example, a later test in the sequence is likely to be accurate as well. We empirically verify that weak dominance holds on real datasets and prove that it is a maximal condition for achieving sublinear regret. We reduce USS to a special case of multi-armed bandit problem with side information and develop polynomial time algorithms that achieve sublinear regret

Sequential learning without feedback

In many security and healthcare systems a sequence of features/sensors/tests are used for detection and diagnosis. Each test outputs a prediction of the latent state, and carries with it inherent costs. Our objective is to {\it learn} strategies for selecting tests to optimize accuracy \& costs. Unfortunately it is often impossible to acquire in-situ ground truth annotations and we are left with the problem of unsupervised sensor selection (USS). We pose USS as a version of stochastic partial monitoring problem with an {\it unusual} reward structure (even noisy annotations are unavailable). Unsurprisingly no learner can achieve sublinear regret without further assumptions. To this end we propose the notion of weak-dominance. This is a condition on the joint probability distribution of test outputs and latent state and says that whenever a test is accurate on an example, a later test in the sequence is likely to be accurate as well. We empirically verify that weak dominance holds on real datasets and prove that it is a maximal condition for achieving sublinear regret. We reduce USS to a special case of multi-armed bandit problem with side information and develop polynomial time algorithms that achieve sublinear regret