Slates

Slates is a multi-slot algorithm that builds upon the ideas of CCB. Please see here for the paper.

It has the following constraints:

1. There is a single global reward
2. Slots have disjoint action sets

Text format

slates shared [global_cost] | <features>
slates action <slot_id> | <features>
slates slot [chosen_action_id:probability,action_id:probability...] | <features>

• slot_id is zero based and required
• chosen_action_id is zero based and refers to the index relative to actions in that slot
• If labeled, every slot must have chosen_action_id:probability pairs
• It is possible to supply the entire actions and probability lists as well for more complex counterfactual experiments

Note: as a single example can span multiple lines it is important to leave empty lines between these examples. If reading from a file, make sure your file ends with an empty line.

Examples

Labeled example

When providing a labelled example the global cost must be supplied and you may either provide just the top action and probability:

slates shared 0.8 | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 1 | <features>
slates action 1 | <features>
slates slot 1:0.8 | <features>
slates slot 0:0.6 | <features>

Or you can supply the entire list of probabilities:

slates shared 0.8 | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 1 | <features>
slates action 1 | <features>
slates slot 1:0.8,0:0.1,2:0.1 | <features>
slates slot  0:0.6,1:0.4 | <features>

Unlabeled example

For an unlabeled example, the global cost and probability list is excluded.

slates shared | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 0 | <features>
slates action 1 | <features>
slates action 1 | <features>
slates slot | <features>
slates slot | <features>

DSJSON format

Overall structure

{
    "_label_cost": 1,
    "_outcomes":[{
            "_a": // <list of integers, or single integer>
            "_p": // <list of floats, or single float>
        },...
    ],
    "c":"..."
}

Context

context:

• Context is similar to CCB, except for the following changes

{
    <shared_features>,
    "_multi":[<action>, ...],
    "_slots":[<slot>, ...],
}

action:

• Action must specify which slot it belongs to

{
    "_slot_id":<slot_id>,
    ...
}

slot:

• Slot has no special fields
• May not specify ids or included actions

{
    ...
}

Examples

Labeled example

When providing a labelled example the global cost must be supplied and you may either provide just the top action and probability:

{
    "_label_cost": 1,
    "c": {
        "shared_feature": 1.0,
        "_multi": [
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            }
        ],
        "_slots": [
            {
                "feature": 1.0
            },
            {
                "feature": 1.0
            }
        ]
    },
    "_outcomes": [
        {
            "_a": 1,
            "_p": 0.8
        },
        {
            "_a": 0,
            "_p": 0.6
        }
    ]
}

Or you can supply the entire list of probabilities:

{
    "_label_cost": 1,
    "c": {
        "shared_feature": 1.0,
        "_multi": [
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            }
        ],
        "_slots": [
            {
                "feature": 1.0
            },
            {
                "feature": 1.0
            }
        ]
    },
    "_outcomes": [
        {
            "_a": [1,0,2],
            "_p": [0.8,0.1,0.1]
        },
        {
            "_a": [0,1],
            "_p": [0.6,0.4]
        }
    ]
}

Unlabeled example

For an unlabeled example, the global cost and probability list is excluded.

{
    "c": {
        "shared_feature": 1.0,
        "_multi": [
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 0,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            },
            {
                "_slot_id": 1,
                "feature": 1.0
            }
        ],
        "_slots": [
            {
                "feature": 1.0
            },
            {
                "feature": 1.0
            }
        ]
    }
}