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Introducing Automated Regression Market Makers (ARMMs): A New Price Discovery Mechanism for Semi-Fungible Assets

Research Collaboration with Hedera Hashgraph and HBAR Foundation to Explore Renewable Energy Market Innovation

BlockScience is researching and developing a novel price discovery mechanism for high dimensional, semi-fungible assets. This mechanism, dubbed an Automated Regression Market Marker (ARMM), has several potential applications in various markets; our first exploration will delve into the use case of sustainable value energy markets, such as Renewable Energy Credit (REC) and Carbon offset/removal Credit (CORC) markets.

Partnering with DLT industry leaders at Hedera Hashgraph and HBAR Foundation, we are embarking on a research project to model and simulate energy credit ARMMs. We will examine the potential for price discovery by primary market makers, as well as supply and demand behavior across assets with multiple attributes. This is the first piece in a series of articles in this joint R&D endeavor.

This piece has been updated since the original release (Oct 27, 2021). The new version of this article aims to differentiate between Automated Regression Markets (ARMs) and the ARMMs referenced above. The term ARM which was originally used throughout this article is more accurately defined as an abstract concept of any market in which the prices of the goods for sale are based on the attributes of said goods and which has the ability for automated transactions to occur. This article is referring to a concrete implementation of an automated agent operating in an ARM, and is thus more accurately referred to as a Market Maker, or here an ARMM. For this reason, ARM has been replaced by ARMM throughout.

What is an ARMM?

In our paper “A Practical Theory of Fungibility”, we introduce the concept of an Automated Regression Market (ARM). An Automated Regression Market Maker (ARMM) is an automated agent deployed within an ARM and is capable of measuring the state of the market, making direct trades, and leveraging the mathematical similarities between machine learning (ML) models and Automated Market Makers (AMMs). This provides dynamic price discovery for assets that are not commodities. Commodities are sets of objects such that the attributes which affect their assessed value, and thus their demand, are equivalent. In a word, commodities are fungible. This concept is central to how existing AMMs work — pooling fungible assets and discovering a price based on its algorithmic curve.¹

ARMMs extend beyond AMMs, enabling semi-fungible assets, such as energy credits or carbon offsets/removals containing varying attributes, to be bought and sold on a primary market ARMM. This enables efficient price discovery for highly complex arrangements of attributes, such as (for energy credits) the type of energy generation, geographic location, etc.

One of the most important observations in this work is that the fungibility of two items depends on both the attributes of those items being offered and the context in which those items are being evaluated. This observation helps us better understand the relationship between supply and demand for markets comprising non-commodity (or “partially fungible”, cf. below) goods.

Item attributes characterize the supply side and we say that goods are distinguishable if they have different attributes. The contexts in which item attributes are evaluated characterize the demand side. We say that goods are substitutable in a particular demand context if the differences in their attributes do not affect their evaluation and thus demand for those goods. We consider goods partially fungible if those goods are distinguishable but substitutable under an evaluation function in the context of some real demand. The substitutability of partially fungible goods changes with the demand context. For example, if a business wants to purchase a solar energy credit produced in the Pacific Northwest in the United States, the asset the buyer wants would not be substitutable for a credit produced in Asia. The ability to identify assets by attributes such as location of production or type of production is not only necessary for many purchasers, but could also have a huge impact on the valuation of those assets.

A scatterplot and histogram representing the distribution of the first two principal components of the simulated attributes. Automated Regression Markets leverage adaptive subspace detection and recursive regression in order to dynamically (re)discover which combinations of attributes are valuable.

Existing Examples of Semi-Fungible Price Discovery

At first glance, the automation of a market capable of buying and selling partially fungible non-commodities seems far-fetched. However, there is precedence for the convergence between markets and ML in both industry and academia.² Housing markets fit relatively naturally into the semi-fungible goods category. Homes are all distinguishable and yet when their attributes are sufficiently similar they may be considered substitutable (prior to purchase — ownership is known to affect substitutability). For these reasons it is possible for the online real estate marketplace provider Zillow to increasingly rely on its AI application, the ‘Zestimate, to drive purchasing decisions.

Zestimate may be one of the earliest examples of a hybrid intelligence that both learns from market activity and creates market activity, but it is very important to observe the performative nature of this model. Zillow has started making offers for homes based on its Zestimate, which naturally affects the market. But the Zestimate doesn’t merely estimate the price of a home, it also creates it by influencing both buyer and seller beliefs about the values of homes. In this way, the Zestimate has been serving as a market maker, even before Zillow got into the business of buying homes based on its estimates.

While there is huge potential in innovating on these technologies, it is always important to consider possible systemic and second order effects, as well as potential unintended consequences whilst introducing machine learning dynamics in markets. On the academic side of this question, leading AI researcher Michael I. Jordan paints us a picture of the synergies between recommendation engines and markets. In particular, he identifies the harms created by naively applying recommendation engines to scarce resources. For example, recommending limited supply goods to many shoppers artificially inflates demand relative to goods which might be substitutable or even superior from some buyers’ perspectives. Similarly navigation apps that recommend low bandwidth shortcuts for many drivers can create severe congestion.

It is the nature of the AI algorithm to compress rich information into a reduced form, but conversely a market is a generator of rich information because it taps into the heterogeneity of a broad base of buyers. If the AI algorithm is allowed to dominate the system it will become stale, as heavy-handed recommendation engines reduce product diversity, and the loss of consumer choice in turn reduces the capacity of the market to elicit preference information from the consumers. We can create better systems with rigorous testing and design validation in the engineering process.

Classes and Instances of ARMMs

As we proceed with our research into ARMM models, we need to make our goals clear. We aim to balance the compression capabilities of machine learning with the discovery capabilities of markets, in order to facilitate new forms of higher dimensional energy markets (among other use cases). As mentioned in our fungibility paper, this is best understood formally within the context of online learning. Our work on economic games as estimators and on constant function market makers (CFMMs) as oracles demonstrate that certain kinds of smart algorithmic pricing models can be interpreted as signal processing operations which learn how the market prices goods and services (in these contexts as commodities) — “contextual commodities”.

The path forward for ARMM research and development requires us to think of it as a “class” where individual “instances” are fit to their particular domain. In ML this includes model selection, feature engineering, metaparameter optimization, ensembling, and other customizations applied by data scientists to fit a particular model to a particular problem domain. In the case of AMMs this includes choosing a particular design pattern, such as Uniswap, Balancer, Curve, etc. These different CFMMs are characterized by different underlying mathematical invariants. But even after one has selected a class of an AMM, there are unique instances with their own assets and other metaparameters such as fees and weights.

This class/instance relationship must be acknowledged as the frontier of ARMM research is extended. Due to its similarity to ML, we understand that developing and maintaining an ARMM can vary widely in difficulty depending on the information the model is being tasked with synthesizing. BlockScience is working with Hedera Hashgraph and the HBAR Foundation’s sustainability initiative to design an ARMM instance specifically for energy credits markets, as energy credit assets provide a good use case of items that have multiple attributes and where value can be greatly affected by context.

An example of ML data clustering by attributes. In an ARMM, clusters like this could represent renewable energy credit attributes and be used in facilitating “matches” of the supply and demand context of semi-fungible assets. (Source:

Why Energy and Carbon Markets are a Great Use Case for ARMMs

Right now, batches of indistinguishable energy credits are bought and sold with very little transparency and auditability. Renewable energy markets are also highly manual, with brokers trading Carbon Offset /Removal Credits and Renewable Energy Credits that may have very different contexts. While those assets are being traded as if they were commodities (fungible), in reality they may have very different values in the market due to where and how the energy was produced, the means of production, the quantity and quality of the equipment being used, and other aspects of their attributes and how those attributes are assessed in different contexts.

With an ARMM, these assets could be separated more granularly as the market, or demand side, could dictate significantly different prices for these semi-fungible assets. Buyers of energy assets, often based on legal requirements in various jurisdictions, require more information and visibility into the supply side. People participating in these markets want to understand which attributes are highly sought after, as well as which are more commonplace, in order to exercise their purchasing power whilst meeting requirements.

Within an ARMM, the semi-fungible goods — “bundles” of various attributes — take on different weights depending on market conditions and the context in which they were produced. This would supply the market with better information for matchmaking across supply and demand parameters — in other words, more efficient markets. Additionally, this capability could provide value by making energy and carbon credits discoverable on a public ledger with a verified link to their auditable source.

Ensuring a CORC or REC is unique and having on-chain representation of carbon offset/removal or energy assets created off-chain, is an incredibly important aspect of this market innovation. A central piece of the Hedera ecosystem and the HBAR Foundation’s Sustainability Initiative is the Guardian³, a fully auditable solution that can provide verification of the energy asset’s attributes. The Guardian provides quality attestations to off-chain data that include decentralized identity, policy driven actions, and fair transaction ordering. These properties provide the means to eliminate recognized data quality issues, such as asset double counting, that obscure both supply and demand, and will be central to the research and development of using ARMMs to automate CORCs and RECs.

An illustration of multiple attributes or parameters that could exist on the supply and demand sides of renewable energy credit markets. The top (green boxes) represent RECs and the bottom (blue) represent CORCs. ARMMs, can distill private preference signals into public price signals while tracking underlying signal changes. An ARMM can “learn” to make more accurate pricing predictions and provide automated matching of supply and demand sides of the market. In the context of market valuation, this same token is semi-fungible as needed for the ARMM.

Potential Benefits and Global Impact of ARMMing Energy Markets

The global energy-as-a-service market size is expected to surpass $106.6 billion by 2026 and with the growing importance of CORCs and RECs, these markets are ripe for innovation. The ARMM mechanism could have huge implications for energy credit markets, and open a new world of possibilities by tying the technology of automated market makers to real world variable assets represented on-chain.

ARMMs could provide automation that would allow massive scaling and expansion of energy markets and trades, accelerating market development and providing the potential for futures markets. Cost could also be reduced for individuals, smaller energy producers or cooperatives who could more easily aggregate diffuse power generation networks to provide collateral or tokenized assets in exchange for access to financing. With more efficient and expanding markets and higher visibility into energy production and attributes, there would be a greater incentive to improve and invest in infrastructure that met higher or more valuable standards, or standards demanded by markets. More visibility in localization could also provide the possibility for locally produced value to be maintained within those boundaries, rather than be extracted to larger markets.

However, as with any technology or innovation, there are many ripple effects that are as yet unexplored — and with any new territory comes potential unintended consequences and systemic effects from new market mechanisms. As mentioned, our goal is to strike a balance between the compression capabilities of ML with the discovery capabilities of markets. As engineers, there are always design trade-offs. This is why modeling and simulation work is incredibly important, and why we use cadCAD to optimize complex system design.

Visualizing higher dimensional spaces with Machine Learning (source:

Modeling ARMMs with cadCAD

cadCAD (short for complex adaptive dynamics Computer-Aided Design) is an open source modeling framework for research, validation, and design of complex systems using computers. This helps individuals or organizations make informed, rigorously tested decisions on how best to modify or interact with a complex system in order to achieve their desired goals.

To begin looking into how ARMMs might produce reasonable predictions of supply and demand interactions and allow for price discovery across multi-attribute energy credits in primary markets, a reference implementation of an ARMM’s algorithms will be developed. Together with data collected from energy credit markets, this reference implementation will create a simulation of market activity with which to test the ARMM’s signal processing capability in such markets. Specifically, we will:

  • demonstrate the energy credit market’s suitability for ML applications and
  • enforce accounting rules, for example, to ensure that an adversary cannot simply bankrupt the ARMM by flooding it with unsellable energy credits.

In parallel, the Hedera ecosystem is developing the core application logic required to deploy ARMMs with business logic and accounting enforced on the Hedera public ledger, such as their recently open-sourced Guardian for validating on-chain claims based on real-world actions.

While the technical requirements will be developed in order to support the deployment of the energy credit ARMM, the result will be generalizable to a wide range of partially fungible, two-sided market applications on their infrastructure. Rather than merely focusing on deploying a wholly custom instance of the ARMM, the Hedera ecosystem is creating an ARMM application design pattern for their infrastructure. This will allow applications to focus on the data science aspects of their ARMM designs, and trust the deployment and enforcement of their market designs to the Hedera network.

In the future, topics such as secondary effects, system level incentives and other potential parameters of the mechanism can be researched to gain insight into how ARMMs might “learn” and operate.

BlockScience looks forward to this research collaboration with Hedera Hashgraph and HBAR Foundation, and sharing more reports from frontiers in market mechanism design, and insights and learnings from further ARMM research and development.

Article by Matt Stephenson, Jamsheed Shorish, Michael Zargham, David Sisson, and Jessica Zartler, with edits by Wes Geisenberger, Sergey Metelin, Jeff Emmett, and Nick Hirannet.


1. In an AMM, the order book of a manual market maker is replaced by pools of assets and an invariant, value preserving, function that relates each asset in the pool to the others. The asset pools are the means by which the market achieves liquidity. The invariant function is the way in which the market determines the relative value of assets. Transactions are individual exchanges of one pooled asset for another. The invariant function calculates the amount of the latter asset that will be exchanged for the former asset, such that the invariant is preserved. AMMs assume that the assets in a given pool are fungible. Fungible assets can be completely described by two attributes, type and amount. Said another way, the only attributes of a fungible asset that matter in any context are its type and its amount. In an AMM, an asset’s type determines the pool to which the asset belongs. An asset’s amount determines the quantity of the asset involved either in overall liquidity or in a particular exchange transaction.

Explainer by Token Engineering Researcher Lisa Tan:

Visual Explainer by DeFi researcher & graphic artist Finematics:

2. Oladunni, T., and S. Sharma (2016), “Hedonic Housing Theory — A Machine Learning Investigation,” in 2016 15th IEEE International Conference on Machine Learning and Applications (ICMLA), pp. 522–527. doi: 10.1109/ICMLA.2016.0092

Shorish, J. (2019), “Hedonic pricing of cryptocurrency tokens”, Digital Finance vol. 1, pp. 163–189. doi: 10.1007/s42521–019–00005-y


About BlockScience

BlockScience ® is an engineering, R&D, and analytics firm specializing in complex systems. Our focus is to design and build data-driven decision systems for new and legacy businesses leveraging engineering methodologies and academic-grade rigor.

With deep expertise in Blockchain, Token Engineering, AI/Data Science, and Operations Research, we are able to provide quantitative consulting to technology enabled businesses. Our work includes pre-launch design and evaluation of economic business and ecosystem models based on simulation and analysis. We also provide post-launch monitoring and maintenance via reporting, analytics, and decision support tools.

About The HBAR Foundation

Founded in 2021, the HBAR Foundation was created to fuel development of the Hedera ecosystem by providing grants and other resources to developers, startups and organizations that seek to launch decentralized applications in DeFi, NFTs, CBDCs, ESGs, gaming and other sectors. In addition to providing funding through a streamlined grant process, the HBAR Foundation acts as an integrated force multiplier through expert support across technical, marketing, business development and other operational functions that are required to scale. For additional information or to apply for funding, please visit or follow the Foundation on twitter @HBAR_foundation.



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