# Tiered Reward: Designing Rewards for Specification and Fast Learning of Desired Behavior

arXiv: https://arxiv.org/abs/2212.03733 · HTML: https://mlsanity.com/paper/2212.03733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 7 Dec 2022.

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations](https://mlsanity.com/paper/1904.06387/) (2019)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [On the Expressivity of Markov Reward](https://mlsanity.com/paper/2111.00876/) (2021)
- [Environment-Independent Task Specifications via GLTL](https://mlsanity.com/paper/1704.04341/) (2017)
- [Direct Behavior Specification via Constrained Reinforcement Learning](https://mlsanity.com/paper/2112.12228/) (2021)
- [Computational Benefits of Intermediate Rewards for Goal-Reaching Policy Learning](https://mlsanity.com/paper/2107.03961/) (2021)
- [Subgoal-based Reward Shaping to Improve Efficiency in Reinforcement Learning](https://mlsanity.com/paper/2104.06411/) (2021)
- [Programmatic Reward Design by Example](https://mlsanity.com/paper/2112.08438/) (2021)
- [Designing Rewards for Fast Learning](https://mlsanity.com/paper/2205.15400/) (2022)
- [Reward Engineering for Object Pick and Place Training](https://mlsanity.com/paper/2001.03792/) (2020)

## Abstract (arXiv)

Reinforcement-learning agents seek to maximize a reward signal through environmental interactions. As humans, our job in the learning process is to design reward functions to express desired behavior and enable the agent to learn such behavior swiftly. However, designing good reward functions to induce the desired behavior is generally hard, let alone the question of which rewards make learning fast. In this work, we introduce a family of a reward structures we call Tiered Reward that addresses both of these questions. We consider the reward-design problem in tasks formulated as reaching desirable states and avoiding undesirable states. To start, we propose a strict partial ordering of the policy space to resolve trade-offs in behavior preference. We prefer policies that reach the good states faster and with higher probability while avoiding the bad states longer. Next, we introduce Tiered Reward, a class of environment-independent reward functions and show it is guaranteed to induce policies that are Pareto-optimal according to our preference relation. Finally, we demonstrate that Tiered Reward leads to fast learning with multiple tabular and deep reinforcement-learning algorithms.