Prospect Theory

Implements Kahneman and Tversky’s Prospect Theory, the Nobel Prize-winning model of how humans actually evaluate risk. It differs from standard expected utility in three ways: (1) outcomes are evaluated relative to a reference point, (2) losses loom larger than gains, and (3) people overweight small probabilities and underweight large ones. The algorithm also includes adaptive drift and epsilon-greedy exploration to ensure catalog coverage.

Algorithm

Config value: "approach": "behaviorAlgos", "sub_approach": "prospectTheory"

Value function:

\(v(x) = \begin{cases} x^\alpha & \text{if } x \geq 0 \text{ (gains)} \\ -\lambda \cdot (-x)^\beta & \text{if } x < 0 \text{ (losses)} \end{cases}\)

Where \(\alpha = 0.88\) (diminishing sensitivity for gains), \(\beta = 0.88\) (diminishing sensitivity for losses), and \(\lambda = 2.25\) (loss aversion coefficient).

Probability weighting:

\(w(p) = \exp(-(-\ln p)^\gamma)\)

With \(\gamma_{\text{gain}} = 0.61\) and \(\gamma_{\text{loss}} = 0.69\).

Prospect value: \(PT = v(x) \times w(p)\)

Exploration (scoring phase):

\(\text{drifted} = (1 - \text{effectiveDrift}) \times \text{normalized} + \text{effectiveDrift} \times \text{uniform}\)

\(\text{finalScore} = (1 - \epsilon) \times \text{drifted} + \epsilon \times \text{uniform}\)

Parameters

• alpha: Diminishing sensitivity for gains. Default: 0.88.
• beta: Diminishing sensitivity for losses. Default: 0.88.
• lambda: Loss aversion coefficient. Default: 2.25. Higher values increase the penalty for under-performing offers.
• gammaGain: Probability weighting for gains. Default: 0.61.
• gammaLoss: Probability weighting for losses. Default: 0.69.
• epsilon: Epsilon-greedy exploration rate. Default: 0.1.
• enableAdaptiveDrift: Enable drift toward uniform distribution for diversity. Default: true.
• baseDriftRate: Base rate of drift toward uniform distribution. Default: 0.05. Also used as the seed score for new offers.
• Processing Window: Time window in milliseconds for historical data.
• Historical Count: Max records to process per update cycle.

Cold Start

Recommendations are always returned. Prospect Theory has strong cold-start handling at both the algorithm and platform levels:

• No history: The RollingBehavior layer assigns uniform random scores to every offer. Additionally, the algorithm itself seeds all known offers with score = baseDriftRate (default 0.05), so even without interaction data the algorithm produces non-zero scores.
• Adaptive drift mixes scores toward a uniform distribution, ensuring catalog diversity from the start.
• Epsilon-greedy exploration provides additional random exploration across all offers.

The scored options are then sorted by arm_reward and handed to the configured dynamic post-score class, which controls the final offer selection and response formatting.

When To Use

• When human decision-making biases should inform the recommendation strategy
• When you want to model the psychological impact of offer rejection
• When rare positive outcomes should be given more weight than raw statistics suggest
• Marketing campaigns where “fear of missing out” (FOMO) dynamics are relevant

When NOT To Use

• When you want a pure statistical optimum (use Ecosystem Rewards)
• When the problem is well-modeled by simple expected value
• When you need fast convergence to a single best offer

Example

from prediction.apis import deployment_management as dm
from prediction.apis import online_learning_management as ol
from prediction import jwt_access
 
auth = jwt_access.Authenticate("http://localhost:3001/api", ecosystem_username, ecosystem_password)
 
deployment_id = "demo-prospect-theory"
 
online_learning_uuid = ol.create_online_learning(
        auth,
        algorithm="ecosystem_rewards",
        name=deployment_id,
        description="Prospect Theory configuration",
        feature_store_collection="set_up_features",
        feature_store_database="my_mongo_database",
        options_store_database="my_mongo_database",
        options_store_collection="demo-deployment_options",
        randomisation_processing_count=5000,
        randomisation_processing_window=604800000,
        contextual_variables_offer_key="offer",
        create_options_index=True,
        create_covering_index=True
)
 
online_learning = dm.define_deployment_multi_armed_bandit(epsilon=0.1, dynamic_interaction_uuid=online_learning_uuid)
 
parameter_access = dm.define_deployment_parameter_access(
    auth,
    lookup_key="customer_id",
    lookup_type="string",
    database="my_mongo_database",
    table_collection="customer_feature_store",
    datasource="mongodb"
)
 
deployment_step = dm.create_deployment(
    auth,
    project_id="demo-project",
    deployment_id=deployment_id,
    description="Prospect Theory demo deployment",
    version="001",
    plugin_post_score_class="PlatformDynamicEngagement.java",
    plugin_pre_score_class="PreScoreDynamic.java",
    scoring_engine_path_dev="http://localhost:8091",
    mongo_connect=f"mongodb://{mongo_user}:{mongo_password}@localhost:54445/?authSource=admin",
    parameter_access=parameter_access,
    multi_armed_bandit=online_learning
)