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Learning the Optimal Policy for Balancing Short-Term and Long-Term Rewards
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Proposes decomposition-based Pareto policy learning (DPPL) to learn policies balancing multiple short-term and long-term rewards under missing long-term outcomes, and links preference vectors to epsilon-constraint thresholds for interpretable selection.
Problem
Learning optimal treatment policies that balance multiple correlated short-term and long-term rewards when long-term outcomes are often missing; linear weighting gives only suboptimal policies when objectives are interrelated or the front is non-convex.
Approach
Decompose the multi-objective policy learning problem into constrained subproblems defined by preference vectors and solve them with a multi-gradient descent (MGDA-style) method to obtain Pareto optimal policies; theoretically map preference vectors to epsilon-constraint thresholds to aid selection.
Key results
- On IHDP (r=0.2), DPPL achieves higher delta W than linear weighting for most of 10 preference vectors, e.g., 56.09 vs 52.33 for the (1,0) vector ordering reported in Table 1 (mixed; many rows favor LW on individual metrics).
- On JOBS (r=0.2), DPPL generally gives higher delta W and lower variance than linear weighting across preference vectors, per Table 1.
- Theorem 1 links preference vectors to epsilon thresholds; the implied minimum short-term reward threshold decreases as the long-term preference weight increases (Table 2).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DPPL instead of linear weighting | MLP policy learning · IHDP, preference vector 1 (1.00, 0.00) | S-REWARDS: 520.860 -> 522.840 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · IHDP, preference vector 1 (1.00, 0.00) | L-REWARDS: 383.950 -> 386.221 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · IHDP, preference vector 1 (1.00, 0.00) | ∆W: 37.307 -> 39.432 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · IHDP, preference vector 1 (1.00, 0.00) | S-VAR: 12.841 -> 14.573 | Hurt |
| Use DPPL instead of linear weighting | MLP policy learning · IHDP, preference vector 1 (1.00, 0.00) | L-VAR: 56.093 -> 52.326 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · JOBS, preference vector 1 (1.00, 0.00) | S-REWARDS: 1612.340 -> 1613.140 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · JOBS, preference vector 1 (1.00, 0.00) | L-REWARDS: 1223.416 -> 1230.918 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · JOBS, preference vector 1 (1.00, 0.00) | ∆W: 155.230 -> 159.381 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · JOBS, preference vector 1 (1.00, 0.00) | S-VAR: 56.502 -> 54.724 | Helped |
| Use DPPL instead of linear weighting | MLP policy learning · JOBS, preference vector 1 (1.00, 0.00) | L-VAR: 88.008 -> 84.846 | Helped |
Surprising findings
- Linear weighting sometimes attains higher individual short- or long-term rewards than DPPL, so DPPL's advantage is mainly in balanced delta W and stability.
Limitations
- Focuses only on discrete (binary) treatments; continuous treatments not handled.
- Relies on causal identification assumptions (strong ignorability, missing-at-random long-term outcomes).
- Experiments use semi-synthetic simulated long-term outcomes on two datasets only.
Experimental setup
Datasets: IHDP JOBS
Benchmarks: IHDP JOBS
Metrics: short-term reward long-term reward welfare change (delta W) variance of short- and long-term rewards
Baselines: linear weighting method
Builds on: linear weighting method for policy learning with long-term rewards MGDA multi-gradient descent epsilon-constraint method decomposition-based multi-objective optimization (MOEA/D)
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