A method of selection that maximizes an expected reward in a contextual multi-armed bandit setting gathers rewards from randomly selected items in a database of items, where the items correspond to arms in a contextual multi-armed bandit setting. Initially, an item is selected at random and is transmitted to a user device which generates a reward. The items and resulting rewards are recorded. Subsequently, a context is generated by the user device which causes a learning and selection engine to calculate an estimate for each arm in the specific context, the estimate calculated using the recorded items and resulting rewards. Using the estimate, an item from the database is selected and transferred to the user device. The selected item is chosen to maximize a probability of a reward from the user device.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of selection that maximizes an expected reward in a contextual multi-armed bandit setting, the method comprising: (a) training a learning and selection engine having access to a plurality of items corresponding to arms in the contextual multi-armed bandit setting; (b) receiving, by the learning and selection engine from a user device, a context in which to select one item from a plurality of items, the plurality of items corresponding to arms in the contextual multi-armed bandit setting; (c) calculating an estimate for each arm in the context, the estimate calculated using a history of past events; (d) selecting an arm that maximizes the expected reward; (e) providing a selection item corresponding to the selected arm for the context received, the selection item transferred to the user device; and (f) receiving and displaying a reward, sent by the user device to the learning and selection engine. 2. The method of claim 1, wherein receiving a context in which to select a specific one of the selection items comprises receiving a search query from the user device. 3. The method of claim 1, wherein selecting an arm that maximizes the expected reward comprises selecting an advertisement that maximizes the probably of a positive response. 4. The method of claim 1, wherein selecting an arm that maximizes the expected reward comprises minimizing a regret parameter. 5. The method of claim 1, wherein receiving and displaying a reward, sent by the user device to the learning and selection engine comprises receiving a response from the user device to a selected advertisement, wherein the response is available for display on a monitor. 6. The method of claim 1, wherein training the learning and selection engine further comprises: randomly selecting items from a plurality of items, the plurality of items corresponding to arms in the contextual multi-armed bandit setting, the random selection of items independent of a context of the item; transmitting the randomly selected items from the learning and selection engine to the user device, wherein the user device transmits rewards back to the learning and selection engine; and recording the rewards received by the learning and selection engine, the rewards corresponding to the items selected and recorded in memory, the memory containing a history of past events. 7. The method of claim 6, wherein randomly selecting items comprises randomly selecting advertisements for products or services. 8. The method of claim 7, wherein recording the rewards received by the learning and selection engine comprises recording responses from the user device to the randomly selected advertisements for the products or services. 9. The method of claim 6, wherein transmitting the randomly selected items from a learning and selection engine comprises transmitting the randomly selected items from a learning and selection engine which is part of an advertisement placement apparatus. 10. An apparatus to provide a selection from multiple items that maximizes an expected reward in a contextual multi-armed bandit setting, the apparatus comprising: a processor that acts to randomly select an item from the multiple items, the multiple items corresponding to arms in the contextual multi-armed bandit setting, the selection of the item independent of a context of the item; a network interface that transfers the randomly selected item to a user device, wherein the user device transmits rewards back to the network interface; a memory for recording the rewards received by the network interface, the rewards corresponding to the item selected and recorded in the memory; a receiver of the network interface for receiving a context; wherein the processor acts to calculate an estimate for each arm in the received context, the estimate calculated using the rewards recorded in the memory, select an arm that maximizes the expected reward, provide a selection item corresponding to the selected arm for the received context; wherein the selection item is transferred to the user device, and the apparatus receives a reward, sent by the user device. 11. The apparatus of claim 10, wherein the processor that acts to randomly select an item from the multiple items comprises a processor with access to an advertisement database that selects advertisements to send to the user device. 12. The apparatus of claim 10, wherein the processor is a component of a learning and selection engine of an advertisement placement apparatus. 13. The apparatus of claim 10, wherein the memory for recording the rewards comprises a memory that records responses from the user device to randomly selected advertisements for products or services. 14. The apparatus of claim 10, wherein the receiver of the network interface receives a search query from the user device as a context. 15. The apparatus of claim 10, wherein the reward, sent by the user device to a learning and selection engine comprises receiving a response from the user device to a selected advertisement.